You only have to register with another State if you are doing business "in" that State, since you are working virtually from your home you only qualify as doing business "in" the State in which you reside. So, no, you do not have to register in any other State.
I don't do business with anybody outside the US so I am not familiar with the laws or tax consequences there. I think the same rules apply as far as registering, but there may be different tax consequences you need to research for receiving foreign money. I would check out
www.irs.gov or talk to a CPA that is familiar with businesses who receive foreign monies.