incorporating in the u.s. for non citizens?
 

possible?

if it is an online business with no physical office, can you pick any state to incorporate in?

Definitely possible. You'd want to go with a friendly jurisdiction like Delaware. Depending on what your plans are it could be a good idea or a bad one.

I'll look into Delaware

can you then hire yourself as an employee? would it ever have immigration consequences, or potential difficulties in crossing the border if you are directly employed by a u.s. company while being a non-resident? tough questions that I guess I need to research

I'm sure it would work