Do international students need to take the SAT and TOEFL to study in the US?
No, you don't need to take the SAT.  The SAT is for students going into undergrad.  Instead, you'll probably need to take the GRE, which is a similar exam for students going into grad school.

Yes, you'll probably need to do the TOEFL, I'd guess.  That seems like a common requirement for international students.

Both of these requirements vary from institution to institution, so you'll probably want to check with the specific institutions that you want to apply to.  Depending on the program you want to go into, you may even have to take a GRE subject test.