I've found that with F#, I get better performance if I do dumb imperative stuff, but keep the side effects within a function. At that point, the functions can basically be "pure" but you can get decent speed.
For example, I usually like using the `Map` data structure, and that's a pretty neat immutable structure and is usually fine for most stuff, but when performance becomes critical, it's easy enough to break into a boring imperative loop with a regular hash map. If I keep everything contained into one function, I usually can avoid feeling super dirty about it.
Yes! That's exactly how you should do it while working with a language that doesn't have a compiler that will aggressively analyze, and rewrite and optimize your code for you. (So, most languages with "heavy runtimes" that support a bunch of dynamic stuff and JITs)
There are basically two points to programming with immutable-first data. One, eliminate certain classes of data race concurrency bugs. Two, less mutable state in a given context makes it easier to reason about.
So, if you're inside a function scope and you aren't launching any concurrent operations from inside that function, you don't have to worry about benefit #1. If you're inside a function (and you're not reaching out for global mutable state), then the context you need to keep in your working memory is likely fairly small, so a few local mutable variables doesn't significantly harm "understandability" of the implementation (in most cases). So, you really don't have to worry about #2, either. Make your functions black boxes with solid "APIs" (type signatures), and let the inside do whatever it needs to make it work the best.
Just because premature optimization is the root of all evil, it doesn't mean we need to jump right to premature pessimization...