Getting into multi-server hosting is a little bit more than you should think about at this point. You can do such things but it's advanced. Work on a multi project solution first, get an understanding of how all that works together, then worry about the more advanced topics.
But to answer your questions:
Yes, there will be three projects, each with its own resulting assembly. Having modular projects isn't so much of a literal implementation as it is an abstract idea. Each project is nothing more than a collection of classes and, for the web project, pages. How you architect/organize them has no bearing on how they work. The organization of pages could give the user an appearance of a "modular" application, but in the end it has now technical benefit. (The exception here is if you divided up a big complex web project into several different ones. Then you'd have a real separation between modules.) Indeed, you could consider that each individual page in a web project is 1 module because with respect to the stateless nature of web applications, each page works independently and apart from the others. They all just happen to live in the same project and application space.
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Peter