What types of problems are better solved in F# than C#?

Is having a combination of F# and C# in a single codebase possible? Is it recommended?

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.

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.