Unless/until a lot more is written in Rust... not much. It uses slightly more base RAM to load the binary. Some of the bloat is things that in C programs would be dynamically linked in - it isn't that Rust is doing more, it's that C gets to share a lot of stuff and Rust has to bring it's own.
I don't know. I wouldn't be surprised that it loaded the whole thing. How could the OS predict how much to load (or wait on)? Waiting for a page to load just for the next function call would be hugely expensive.
