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Can I use a format string in a URL to navigate to web page, replacing the specified portion of the URL?

I'm interested in creating some sort of simple C# application takes a user string and passes it into a target portion of the URL. For example, since user query is visible in the page URL DuckDuckGo
Example:
https://duckduckgo.com/?q=web+browsers&ia=web
In this case, the URL shows that I searched for "web browsers". I would like the user to be able to pass any string to the application (via some kind of prompt that appears with the application is launched), and then launch a web browser and navigate to the target URL with the user input inserted into URL where the query is specified. (i.e., https://duckduckgo.com/?q=operating+systems&ia=web), where the user entered the string "operating systems".
So I would like to know which type of C# application to use that can interact with OS (Windows 10) and how to write the code for the the format String and the user prompt. Any guidance would be appreciated.

Your question is very broad so the best that can be done is give a broad answer. You mention "application" and "interact with the OS", so I'm assuming a native application, not a web app. A quick way to pull this off would be to Google for "C# Web Browser Example"; there are plenty of applications out there with well-explained source code that will answer your question:
So I would like to know which type of C# application to use that can
interact with OS (Windows 10)
As for the string replacement, Armine already pointed that out in his previous post. A simple textbox on your form, passed to some parsing code with string replacement, will do the trick for building the URL. The resulting URL is then passed to the web browser control you've used in your C# application; the URL will be one of the properties of the control.

The idea is to take what user typed as a string, and then create another string which will contain the words of that string, separated by the plus character (+)
String what_user_typed=" javascript jquery";
String query=what_user_typed.Replace(" ","+"); // A space represents a new word
String url="https://www.google.com/search?query="+query
After creating the url you can then use a webbrowser to open that url

I have not executed this but think this is what the logic should be.
string input = "operating system";
string destinationURL = $"https://duckduckgo.com/?q={input}&ia=web";
string formattedURL = HttpContext.Current.Server.UrlEncode(destinationURL);
System.Diagnostics.Process.Start(formattedURL);

How to maintain the right URL in C#/ASP.NET?

I am given a code and on one of its pages which shows a "search result" after showing different items, it allows user to click on one of records and it is expected to bring up a page so that specific selected record can be modified.
However, when it is trying to bring up the page I get (by IE) "This page cannot be displayed".
It is obvious the URL is wrong because first I see something http://www.Something.org/Search.aspx then it turns into http://localhost:61123/ProductPage.aspx
I did search in the code and found the following line which I think it is the cause. Now, question I have to ask:
What should I do to avoid using a static URL and make it dynamic so it always would be pointing to the right domain?
string url = string.Format("http://localhost:61123/ProductPage.aspx?BC={0}&From={1}", barCode, "Search");
Response.Redirect(url);
Thanks.

Use HttpContext.Current.Request.Url in your controller to see the URL. Url contains many things including Host which is what you're looking for.
By the way, if you're using the latest .Net 4.6+ you can create the string like so:
string url = $"{HttpContext.Current.Request.Url.Host}/ProductPage.aspx?BC={barCode}&From={"Search"}";
Or you can use string.Format
string host = HttpContext.Current.Request.Url.Host;
string url = string.Format("{0}/ProductPage.aspx?BC={1}&From={2}"), host, barCode, "Search";

You can store the Host segment in your AppSettings section of your Web.Config file (per config / environment like so)
Debug / Development Web.Config
Production / Release Web.Config (with config override to replace the localhost value with something.org host)
and then use it in your code like so.
// Creates a URI using the HostUrlSegment set in the current web.config
Uri hostUri = new Uri(ConfigurationManager.AppSettings.Get("HostUrlSegment"));
// does something like Path.Combine(..) to construct a proper Url with the hostName
// and the other url segments. The $ is a new C# construct to do string interpolation
// (makes for readable code)
Uri fullUri = new Uri(hostUri, $"ProductPage.aspx?BC={barCode}&From=Search");
// fullUrl.AbosoluteUri will contain the proper Url
Response.Redirect(fullUri.AbsoluteUri);
The Uri class has a lot of useful properties and methods to give you Relative Url, AbsoluteUrl, your Url Fragments, Host name etc etc.

This should do it.
string url = string.Format("ProductPage.aspx?BC={0}&From={1}", barCode, "Search");
Response.Redirect(url);
If you are using .Net 4.6+ you can also use this string interpolation version
string url = $"ProductPage.aspx?BC={barcode}&From=Search";
Response.Redirect(url);
You should just be able to omit the hostname to stay on the current domain.

Kentico - Using punctuation with AuthenticateUser

We are currently using version 7.0 of the kentico API to authenticate users into our system.
The following code is used to gain user details from the database and authenticate users.
UserInfo objUserInfo = AuthenticationHelper.AuthenticateUser(username.ToLower(), password.ToLower(), CMSContext.CurrentSiteName);
This has primarily been working correctly, but we are having issues with usernames and passwords that contain any of the following characters.
" ! # ' / \ > < * -
Is there any settings that I need to be aware of (web.config or otherwise) that would stop the API from accessing an account where a username or password contained special characters?

Looks like there is according to the documentation. Check into this web.config key:
<add key="CMSUserValidationRegEx" value="([A-Za-z0-9-]+)" />
Sets custom regular expression used for user name validation (used when new accounts are created or when existing usernames are modified).
The default value is "^[a-zA-Z0-9_\-\.#]+$".
If the CMSEnsureSafeUserNames key is set to false, the following regular expression is used by default: "^[a-zA-Z0-9_\-\.\\#]+$".
The only thing I can't tell for 100% is if it is purely for the AD Import of users or ALL users. It looks to be used on any call to ValidationHelper.IsUserName, so it is pretty safe to assume it is in play everywhere.
Source: http://devnet.kentico.com/docs/7_0/devguide/index.html?web_config_parameters.htm#forbidden_chars_users
Also the internal message when you try to create a user with those characters complains too. SO this would tell me that it is in play everywhere.

Replacing special characters in web.config using Intelligencia UrlRewriter

I have an article based website where users can login, post articles etc.
The url I am using for a registered user looks as follows (only example):
http://example.com/Author/1234/Screenname
Like you can see, I am passing through the ID (1234) and using the users screen name.
The Problem
Passing the ID is 100% fine, but once a user has a special character or anything that is not A-Z, it will return a 404 or a Bad Request page.
Problematic URL
See /Screen.name - I want to replace special characters, coz it will cause a Http error.
http://example.com/Author/1234/Screenname.
I want to use the Intelligencia UrlRewriter in the web.config (or any other global solution, e.g. global.asa) to replace special invalid url characters.
My current web.config rewriter code:
<rewrite url="^~/Author/(.+)/(.+)" to="~/Contributor_Profile.aspx?auID=$1&auN=$2" processing="stop" permanent="true"/>

Try this in your web.config
<httpRuntime relaxedUrlToFileSystemMapping="true" />

Safe Process.Start implementation for untrusted URL strings

My goal is to safely open a web page in a users default browser. The URL for this web page is considered "untrusted" (think of it as a link in a document opened with this software, but the document could be from anywhere and the links in it could be malicious)
I want to avoid someone passing "C:\Windows\malicious_code.exe" off as a URL
My current thought is to do something like this:
Uri url = new Uri(urlString, UriKind.Absolute);
if( url.Scheme == Uri.UriSchemeHttp || url.Scheme == Uri.UriSchemeHttps )
{
Process.Start(url.AbsoluteUri);
}
Am I forgetting about anything else that my 'urlString' might contain that makes this dangerous (e.g. a new line character which would allow someone to sneak a second process to be started in after the URL or a possible execution of a relative executable starting with http)?
I'm pretty sure both of those cases are handled by this (as I don't believe Process.Start allows you to start two processes as you would in a BATCH file and this should only allow strings starting with http: or https: and are valid urls)
Is there a better way to do this in C#?

What you want to check is the scheme of the url (i.e. ftp://, http://, file://, etc.) Here is a list of schemes: http://en.wikipedia.org/wiki/URI_scheme#Official_IANA-registered_schemes
To find the scheme of a URL, use:
Uri u = new Uri("C:\\Windows");
String scheme = (u.GetLeftPart(UriPartial.Scheme).ToString());
For me, the above example gives file://. Just check the scheme, using the code above, and reject the ones you want to filter. Also, surround the parsing with a try-catch block and if an exception is caught, reject the URL; it can't be parsed so you shouldn't trust it.
If you want to ultra-paranoid-safe, you could always parse the URL using a URL parser and reconstruct it, validating each part as you go along.