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C# Sidescroller starting advices

since this is my very first time trying to make yet simple but useable sidescroller I'd like to ask some questions and hopefully gather ideas to make a good engine that can change the position of an Image in the form depending on X position of the drawn game character. I'd basically like to recreate just few seconds of a Mario game.
The starting Idea (correct me if it's wrong / poorly performance / whatever) would be to create a picture long in width and whit fixed height and upon the press of, for example, A or D keys, the drawn character moves till a certain X point, after that, character gets locked in place and if the key is still pressed, the background image starts moving.
But the problem there would be the fix for collisions, would be possible to check for the X position of the drawn background picture and set "collisions" accordingly for the character?
Other questions : why picturebox should be avoided at all costs and use the form itself instead ? Placing the greater part of the classes methods inside a timer_tick event is the wrong approach ? I read somewhere that the best way to do games of this kind would be relying on infinite loops in the forms main method, but I simply cannot even think how this could possibly works, taking in count all the times we may need to get out of the loop and do different code in different places.
Any other different ideas/approach and direct links to further explanations would be greatly liked
Edit : yes i'd like to improve with windows forms before moving to xna/unity

Assumption: You want to make a little game and its your first time working with moving graphics and you're working with WindowsForms. Suggestion: try using a more advanced framework such as MonoGame or XNA and working your way through introductory documentation and tutorials. Also WPF has a more advanced graphics platform for doing things like drawing and 3D, you may want to give that a shot.
To expand on my comment a bit.
Windows Forms and GDI (the tech behind drawing) aren't meant for this kind of use. When GDI was created its purpose was essentially drawing lines and fonts on the screen. XNA is a really good framework for learning the basics up to professional design. Unfortunately the XNA framework is no longer supported by Microsoft and as such MonoGame is the recommended development route for managed .NET 3D and 2D game development.
The WPF provides basic access to Direct3D and Direct2D, and has 2D and 3D shapes and animations built into the framework and is what WPF is based on.
But you also have the choice, if need be, to create an XNA component and embed it in a Windows Form as demonstrated in these two tutorials.
XNA in Windows Forms I
XNA in Windows Forms II
Also using a Windows Forms Timer isn't recommended because they are unreliable. The .Net Framework provides a 'Server Timer' and a 'Threading timer' that can be used as well.
If you are really keen on using GDI for a game may I recommend reading about the basics of game programming (I think there are a few XNA docs on the subject) that should guide you on things like the basic run time loop, getting input, and simple physics.

Program architecture for Windows 8 C# & XAML app featuring graphics

If I'm looking to create a game that doesn't necessarily run full screen, but simply needs to feature 2D/3D graphics somewhere in a portion of the screen, what's my best approach?
Some specific questions could be:
What component would the rendered area use?
Are there any game libraries I could leverage for the rendered area?
What would be the most "pure" or "canonical" stack according to Microsoft to use here?

Omega --
Visual Studio 2010 and 2012 are Both WPF apps. WinRT is for Tablets / Mobile. WPF is certainly NOT outdated.
If I were you I wouldn't render everything out the way canvas forces you to, it might be a better approach to have the center item be a UI element named Frame, which is the base element for all UI related content in WPF.
In this way you would be able to leverage all of the possible types of controls in the Frame whether you decided that An ImageSourceType or Canvas is more applicable to a particular features of the game.

Depending on how you want to draw graphics, you could use (but are by no means limited to):
Canvas - which would be totally appropriate for slow moving games. This way you get the benefit of the various WPF layout routines and can define objects inside the scene in XAML/vectors as well.
WPF supports 3D graphics (using Direct3D on the backend) so you could probably set up an orthogonal projection matrix and treat it like a Direct3D context (with the WPF API). I don't have enough experience to know how slow this is compared to D3D, but it's certainly easier (built-in "scene graph" like support from the XAML architecture, for instance).
If you want to go whole-hog with Direct3D you could use SlimDX, which has a WPF shim that I've used in the past, as well as another third party control. There may be other libraries available as well.
Direct blitting to/from a Bitmap using WriteableBitmap (see WriteableBitmapEx for a third-party version with a much friendlier API) or similar.
There are probably a lot of other options too. My preference would be for using Canvas initially if it's a slow-paced game that doesn't need super-fast frame rates (the layout work does incur a fairly substantial overhead, but it's less work and may be easier to get looking exactly the way you want).
If you want absolute control and speed, use D3D through SlimDX, but this is a pretty hefty learning curve if you're new to it.

Creating an analog clock on C#

I intend in creating a few analog clocks on Visual Studio 2008 (C#) for a school project, but I'm am still a bit unsure on how show I do it..
Should I import an image of a pointer and then add the codes to it to make it spin?
Or should I use some sort of code to actually draw the pointers and move them?
EDIT:
Been looking around the internet but I am not sure on how should I begin... never used any properties on how to actually draw something on C#, can someone tell me how should I proceed to make an analog clock?

It will be easier to draw the hands than to rotate images of the hands, especially since you will need one image for each hand and the images will conflict with each other.

However you choose to do the hands (images or xaml shapes) you'd then animate them with the RotateTransform Msdn has a sample too
You could also use databinding and a timer to change the rotation every second

How would one go about creating one’s own graphics effect in WPF?

I have an Image object in my application which the user can drag around. The object displays an image which is partly transparent, so the window background (which is itself a bitmap) can be seen through it.
I want to add a graphics effect to this object. Assume that I already have an algorithm for this effect — that’s not the issue. The issue is how to get this algorithm into WPF.
So I tried to look at how DropShadowEffect works, but the implementation displayed in Reflector is empty. I also tried to look at what methods from the abstract classes Effect and ShaderEffect I should override and there doesn’t seem to be anything related to actually rendering an effect.
So how do I create my own effect?

The best and fastest way is to use pixel shaders (supported starting with WPF 3.5 SP1 I think) . It will require some shader language (HLSL) knowledge, though :-)
Here is a tutorial: How Do I: Create Custom Pixel Shader Effects for WPF
a library on codeplex: Windows Presentation Foundation Pixel Shader Effects Library
an article with .NET 4 information (including Sliverlight support which has it too): SilverShader – Introduction to Silverlight and WPF Pixel Shaders

A very cool tool (and resource) is Shazzam it will help you to create the effects and it contains a nice tutorial.

Is it practical to port code from Flash to C#?

My goal is to gain a better understanding of the characteristics of C#, and become more comfortable creating simple apps. I am fairly competent with Flash (Actionscript 3), and found an old Tic-Tac-Toe game I'd written. I started wondering about porting this code into a C# application. Not knowing much about C#, I'm wondering how difficult the migration would be.
On the one hand, the underlying game logic is syntactically similar, and therefore would be easy to port.
However, as far as the graphics are concerned, I don't even know where to begin. So far, I've only exposed myself to Windows Forms and Console apps in C#.
I'm wondering if these Flash concepts have similar analogs in C#, or if the procedures and syntax are radically different:
Placing graphic elements on a stage
Rendering lines from start/end coordinates
Event listeners on movie clips
Swapping the image inside a graphic element (or, in my Flash version, nextFrame() in a movie clip)

You may want to try developping your little game using Silverlight. Silverlight applications, coded using C# and Xaml, are pretty similar in form with flash applications, and you should find everything you need without trouble.
So I suggest you download the Silverlight SDK (free) and give it a try.

Firstly, Flash is to WPF (close enough) as ActionScript is to C#.
The WPF/Silverlight model is much more similar to Flex that it is to Flash. Everything is added to the UI tree as a object, even lines.
Likewise, adding event handlers to controls (like a button click) can be done in the "code behind" (the code that lives with the view), but the recommendation is to use the MVVM pattern. If you are new to the concepts of separation of concerns and unit testing, feel free to start with the simpler "code behind" method.
While WPF and Silverlight are very similar, I'd recommend starting with Silverlight as the SDK and available samples are richer. You can easily move onto WPF later on (though porting an application from Silverlight to WPF is not automatic).
Swapping images, as you mentioned, would be done via "Visual States" in Silverlight (or possibly changing the image reference, which is more "hacky").
Have a look at the following links to get started:
Learn # Silverlight.net
Silverlight on MSDN
Shapes and Drawing (Silverlight)

If you're looking specifically to do games and the like, you may wish to look into the free XNA framework. However, there will be differences as Flash gives you far more ability to "set up" things beforehand and modify them.
Placing graphic elements on a stage
If you go the XNA route, you will be drawing sprites using the spritebatch, you tell them where and how to draw and that's where they will go
Rendering lines from start/end coordinates
In windows forms you can do this via a simple System.Drawing call, however if you wish to do this in XNA, you will either have to make a 1 pixel square and stretch/rotate it to what you want, or use 3d primitives (Though this will limit you to a 1 pixel line)
Event listeners on movie clips
Look into delegates, but there isn't really an equivalent for movie clips to my knowledge
Swapping the image inside a graphic element (or, in my Flash version, nextFrame() in a movie clip)
This is fairly simple, depending on what you mean. If you want to, say, animate a sprite. You can do this by moving the source rectangle or changing the texture of the spritesheet. If you mean the screen as a whole, this is mostly handled for you provided you use the spritebatch. In windows forms you'll have to do more of it yourself, but the base concepts are the same.
Overall it's not that bad, but if that doesn't sound appealing check out Silverlight. It's basically C# styled flash so you may find the transition easier.
Good luck and hope this helps.