(1) Higher order functions are pretty much the same as all the other languages you mentioned, using closure syntax? What was the problem you ran into?
(2) In such situations the compiler (type system or borrow checker) is telling you that what you wanted to do has hidden bugs, and therefore refuses to compile. Usually that's a good thing.
(3) &dyn Trait
(1) Oh sure, the syntax is easy. Getting it to borrow-check is somewhere between insane and impossible. As I said, I've had friends who are actual Rust experts give up trying.
(2) No, it stems from a compiler limitation (imposed in large part by the need for static memory layout), not because there's anything intrinsically buggy about doing this.
(3) Look up "dyn-compatibility", for the largest, but not the only, problem with doing this.