Is it possible to be admitted to a top-tier US university as a non-US resident (I'm Swedish)? How does that work with SATs and stuff then? Also, is it possible

Is it possible to be admitted to a top-tier US university as a non-US resident (I'm Swedish)? How does that work with SATs and stuff then? Also, is it possible to be admitted if one is outside the typical age range of applicants (ie 18-19)? I just don't know how these things work for you in the US, so I had to ask :)