Yes, it is quite possible. I was a very advanced application like that, a whole vector drawing application.
For example, please see this open-source project:
By the way, no server side is used at all. Load source code and try, just out of curiosity.
Other approaches use server-side, and of course it can be ASP.NET. Could be somewhat slow.
What tools? Your brain. Actually, a good amount of brain. I think all the detail would go well beyond the forum format.
As to Paint: don't develop such or similar thing. Nobody needs it, including Microsoft Paint.