Easy code is much easier in f#, a lot of the time. Hard code is usually easier in f# due to the type system helping a lot. F# is also a lot more concise.

And yes, you can combine them, but afair, only in terms project boundaries. (You can include a c# project in an f# one and vice versa). There are a few cases where it's quite useful. For example, rewriting a part of a big project in f# to leverage the imperative shell - functional core architecture. Like rewriting some part that does data processing in f#, so that you can test it easier/be more confident in correctness, while not doing a complete rewrite at once.

Sort of like rust parts in the linux kernel.

I don't think it's a matter of the type of problem and I always found it weird how F# is being framed as being only useful for "math-heavy" problems.

What matters is what libraries you are gonna use for your solution. If most of them are C#-only and don't have an F# equivalent then you'll lose the ergonomics and conveniences that make F# so easy to work with.

All types of problems. F# can do almost anything C# can do and with less ceremony. The quote I like is that once you get comfortable with F#, switching back to C# is like "having to fill out government forms in triplicate".

It's very possible, even encouraged when you have workloads that call for it. F# is a great functional language, so it's good for parsers, compilers, etc. The support for units of measure is also really cool, making it great for scientific computing.