When it comes to making a browser game, there isn't really a point to asking "is it possible to do ____?". Unless you're talking about technological restrictions(like "is it possible to render 3d graphics at 65 FPS accross all computers inside a browser window?"), the only limitations on what's going to be possible or impossible regarding gameplay will be based on how you implement your idea.
You might want to find a free piece of web server software like
Apache, which you can then setup and run off of your computer so that you can do all of your testing and debugging without actually finding a web host. You'll also want to install MySQL or some other database alternative so that you can store player information.
Regarding programming languages, the most common I've heard of being used for browsergames are PHP, Perl, and ASP. There are other options though; I've heard of people using Ruby and Python too. You just need to pick the one that you like best.