My supervisor assigns to me many tasks a week and wants them finished in a short period of time, it's been a while now and i feel a bit exhausted. Is this scenario common amongst CS PhDs in the US ?
Having a lot of work is common. Feeling overwhelmed and stressed is common. Should these be acceptable? Entirely up to you.
Time management and resource allocation are some of the biggest skills you will perfect during the PhD. Hopefully you can chat openly with your advisor about your concerns and discuss what an acceptable amount of work to accomplish is. If you are new, your advisor is also learning how much they can push you and what your strengths and weaknesses are. If you are later in your PhD, this advisor/student relationship should develop into more of a collaboration with the advisor providing more oversight and guidance than goals and deadlines (although many will still do that).
It's also a HUGE learning journey, meaning there are weeks when you will have no results to show, but SHOULD have learned a lot and can more intelligently speak about some aspect of your work/field.