Can the equivalent of eval and exec exist in a compiled language? If so, how would they be compiled (roughly speaking)?
For starters, python is a compiled language, it just does the compilation at runtime.  That being said, all that you need to do to implement eval in any other compiled language is to be able to run the compiler (and dynamically load object code) - you can do this in Python (and a litany of other languages) easily because the compiler is an integral part of the runtime.  There's technically nothing that stops a program written in C from invoking the compiler and loading the result at runtime (using dlopen), it's just not a common occurrence because the C runtime doesn't require a compiler, so most users don't have one.
If Python's exec and eval were compiled?