Binary size very much depends on your settings. Rust does not optimise for a small 'hello world' by default, but it's very possible to get small binaries from it if that's a priority for you (for example, the default debug build neither optimizes for size nor strips debug information, as well as statically linking the standard library). Compile times are more sticky problem and most ways to improve it basically involve avoiding certain language features and libraries.
Same. I was about to jump into learning Rust and make it my no.1 language for new projects instead of node.js + TypeScript, but once I learned about the slow compile times I stopped that thought immediately.
For me it was a choice between slow compile times now when it’s safe, or unbounded time solving security and stability issues later when it’s critical.