'Yes-man' doesn't just refer to men, you can use it for both genders.

That is a complex question. "Yes-woman" is a word and is used for females only. But it is also okay to use "yes-man." There are many words like that, like "lumberjack." While it is only for men, it is also used to describe women.

A "yes-person" is neutral. Sycophant, toady are also good, as is groveller, arse-licker, brown-nose.... going from more to less polite. Personally, I would say "toady".

"Sycophant" is gender-neutral, as is "lackey" and "kiss-ass".