> But they don't mutate data and hence every function call creates a new data in memory taking up space.

Well, only if you mutate the data. And even then, most functional languages provide persistent data structures that allow efficient sharing of the unchanged parts of the data structure.

> Now my question is where do I learn about these nitty gritty's? Should I read about compilers more? Or systems? Or what?

I'd recommend choosing a functional language and an imperative language and learning both.