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Deploying ASP.NET Core Web API and ASP.NET Core with Angular in a subfolder (1&1 Windows Business Hosting)

I've acquired a 1&1 Windows Business Hosting which allows to deploy ASP.NET Core applications (so yeah, I have no access to IIS solutions of building as application stuff or that kind of things I've seen in other posts). I wanted to deploy a web and an API in different subfolders within the 1&1 server I've acquired.
What I want to achieve is the following:
Imagine that my domain is https://myDomain. com.
If a user access directly that URL he should see a specific page of the Angular Web App. However, if the called is https://myDomain. com/api/controllerName it should do whatever I have programmed in that controller of the Web API.
I want to have the folder structure something like this:
But it is also valid if I manage to get it like this:
Is any of these two cases even possible to be done? If possible, how I should proceed for being able to do it? I don't have a lot of knowledge in these topics related to web deployment.
What I have managed to do up until now:
If I deploy just the ASP.NET Core Web API outside the subfolder it works with no issues. If I deploy just the ASP.NET Core with Angular outside the subfolder it also works. My issue is that I'm unable to get them both to work at the same time when at least one of them is in a subfolder.
Alternatives on how to achieve this are also welcome!
Thanks in advance :)

You can deploy ASP.NET Core Web API and ASP.NET Core with Angular in two folders as shown in the image below.
These two folders are virtual directories in IIS. If you want to specify which app to access by default, you can modify the rewrite rule in web.config under the wwwroot folder.

How to run ASP.NET web api from github

I am new in asp.net and angular development.I dont know how to run asp.net web api from github. As we run angular code by using "ng build --prod --base-href https://ownername.github.io/repositoryname/ so i want to know could we run asp.net web api by using such kind of any command or something other which is used for this.
Basically i want to run my project on network i tried by IIS server but no result is showing so now i want to try github process
Help would be appricated

asp.net core apps have to run in a .net core process on a server so the hosting environment needs to specifically support this. a variety of web servers can be configured to proxy the requests. Unfortunately, I don't think GitHub allows running app processes for asp.net core.
However you ca easily deploy to azure with even a free account
https://learn.microsoft.com/en-us/aspnet/core/tutorials/publish-to-azure-webapp-using-vs?view=aspnetcore-2.2

Building a remote command for Elpis in C# through HTTP API

I am helping to build Elpis, which is an open source pandora music player, built with C# and WPF.
Now what i want is to add an HTTP API so that the user may control the program through a browser, like play/pause, like/dislike the current song.
The point afterwards is to control the program through a mobile device accessing the HTTP API.
How exactly should i build the HTTP API so that it can control it?
Github for the project: https://github.com/adammhaile/Elpis

Without knowing why exactly you want the user to control a GUI application via the browser, it's hard to give you good advise.
Assuming you are running your GUI on Windows, take a look at OWIN and the project Katana. They allow you to easily host HTTP interfaces in your own application.

It may be overkill for your project but I would suggest using ASP.NET Web API so that you can build backend web services.

The easiest way to do what you want, assuming you really want to "control the GUI remotely" is to just install TeamViewer on your PC and on your mobile device. Then you could remote in and completely control your GUI.
But I what I think you're after is something more like Google Music. Where you can stream your music through the Internet and onto your mobile devices. If this is the case, I recommend you look at the ASP.NET Web API.

It's not hard to build a web server in C#. You can embed it into your application, and expose parts of your application to HTTP endpoints as an API. You can use the HttpListener class which is part of .NET, and do everything from the ground up yourself. Or you could use something like Nancy, which is a lightweight framework that provides a lot of useful scaffolding like URL routing.

Ended up using Kayak(https://github.com/kayak/kayak) for my self-hosted API.
The example of integration can be seen here:
https://github.com/adammhaile/Elpis/blob/master/Elpis/WebInterface.cs

ASP.NET website to be deployed on Windows Azure with databases

I know this is a very common question and I could find several answers, but I think my situation is a bit different.
So, I have an ASP.NET Website (NOT a web application), built using "Web forms". Its a very simple website which does bunch of REST calls and talks to the SQL Server 2008. Can you please help me finding a step by step guide to deploy the same on Windows Azure using VS 2010? As of now, the website runs fine on a traditional web hosting server.
So far what I am getting are approaches which use MVC (and using ASP.NET web application, not website). I don't think that I should be concerned about MVC at all? Does a website vs. web application aspect make a difference? If yes, do I need to convert the website to web application?
There's a lot of content on web, so I am a bit confused given my condition. Can someone please put me in right direction? Thanks a lot.

You'll need to convert your Website project to an ASP.NET Web Role project, whether you first convert it to a ASP.NET Web Application or not doesn't really matter. The rest of the tutorial you already linked to applies just fine.
There's no need to look at ASP.NET MVC, It's a different technology than web forms, and there's no need to move to it in order to get your site hosted on Azure.
As for your database, unless you host that yourself in a VM-Role or somewhere else (and connect it using Azure Connect), you'll need to convert it to Sql Azure or Azure Table Storage. SQL Azure is largely compatible with SQL Server, but there are a few features which are unsupported.

How to configure and debug a web application using MVC and WebForms

I have an existing ASP.NET web application that I'm converting to MVC 1.0. The site started out with one goal. However, over time our sponsors are asking for more functionality and it is obvious that MVC would be our best route due to the new requirements. I've dabbled in MVC over the last couple of months and have a pretty good grasp on it all works. The problem that I'm faced with now is that the meat of our existing web application makes extensive use of a 3rd party tool that only works within ASP.NET WebForms.
The solution that I'm working on is to have two web applications running on the server. The one application would be our existing WebForms app and is solely used to expose the above mentioned 3rd party tool's functionality. The other application will be our main portal that will act as the new site. When the user wishes to interact with the 3rd party tool, I want to be able to load an iFrame on the appropriate Views that links the user to the other application and will then allow them to interact with the WebForms site. Does this sound crazy?
The number 1 problem that I'm faced with right now is how to configure my solution make the MVC application talk to the WebForms application. Every time I run the solution, a different port number is assigned to the two applications and I can't figure out how to configure my iFrame "src" properties correctly. Of course, I can't add the WebForms application to my MVC applictions' References, so I'm stumped!
Any help would be greatly appreciated...

If the port issue is the only problem, you can run both of them in IIS under a fixed virtual application.
But the ASP.NET development server also has the feature to fix the port to a specific number and not randomize it each time.