If Gecko is ever able to get rid of all of it's C++, it won't happen for quite a while, that will be an enormous undertaking. I would expect, if Rust is successful enough that that is feasible, then by that time there would be multiple different Rust implementations, and some of them may be written in pure Rust.

There's no fundamental reason that the Rust compiler has to be dependent on LLVM. It's just a good strategic decision as it allows the Rust developers to focus on the parts of the compiler that are unique to Rust, and use a well tested backend with lots of existing optimizations and targets for the parts that aren't particularly unique to Rust. There is actually some discussion already of using a faster, pure-Rust backend for debug builds, and maybe far in the future for release builds as well (https://internals.rust-lang.org/t/possible-alternative-compi...).

The relevant parts of the LLVM toolchain could be ported to Rust. IIRC Rust originally bootstrapped with OCaml.