Imho they are about the same, or maybe TS is even a little bit better, since you can really have freestanding functions (C# has either (static) member functions or delegates). The Javascript ecosystem probably also leans a bit more towards FP style in the mainstream (with lodash, ramda, redux, etc.) than C# does. What are you missing in particular? I guess the main thing for both is tail recursion.
Does TypeScript have any kind of "do notation" or "comprehension" syntax? LINQ is not the best by any means but it does seem like a big improvement over nothing.
No, it doesn't. I guess that's because monads are not considered idiomatic typescript. And for the special case of async programming there's async/await support.