2. There are already several web frameworks, in various stages of earliness. See [1]. I don't think it will ever be a good idea to write Rust client-side though (even though I believe there is an emscripten backend for it, so it's possible).
3. I see a very bright future for Rust. It could use some ergonomic improvements (but it's miles ahead of C++ even now, mind you), but is otherwise a very well designed language that fits very snuggly in its niche. And it has some very strong backing from Mozilla. I expect it will slowly take over large amounts of territory from C++ and possibly from C, as these developers start to realize the benefits of Rusts safety guarantees. It's also quite unique in that its safety entices many higher-level (python, ruby, C# etc.) developers into trying system programming, which could be really transformative to the system programming scene. For example, one thing that has already come out of this is the cargo package manager, which is similar to npm, bundler etc. but (before cargo) had yet to find its way down to the lowly systems programmers. Many (former?) C++ developers actually tout it as one of the major benefits of Rust.