Can I see how many times I watched a movie on Apple TV?

That detail is not retrievable.

Most content has a status for Unwatched, Partially Watched, and Watched (to the end). Partially Watched doesn’t signify a first watching.

how do i see what movies i have rented

how do i see what movies i have rented

See your purchase history for the App Store, iTunes Store, and more - Apple Support