involvement

These are involved in sga but not most involved in sports, dance, other, etc...

So Theta has SGA presence despite not being affiliated?

Yes, Theta has members that are apart of SGA.

Theta is not affiliated with the Machine. However, SGA is a completely different thing... SGA is open to anyone on campus, not just Greek members. The Machine has some power over who gets positions, but they mainly focus on the president position and they make sure that whoever "wins" that position is a part of a Machine affiliated Greek organization (i.e. Lillian Roth - Chi O, Jared Hunter - Theta Chi, etc). The other positions are really open to whoever based on merit and actual votes. So yes, Theta does have a handful of SGA members despite not being Machine affiliated.

There goes the girl who stalks XO again. No houses have rules like that. There are too many positions to be filled in any house to limit them to in state only.

There aren' explicit rules that say only girls from certain areas can hold certain positions within their house, but I know that there's definitely a huge bias. It isn't really the chapter president who has the bias it's the alums... Alums want to see predominately Southern girls in more important positions within the chapter and I know this is the way it is in at least two Old Row houses. However, even though there may be a bias there are still girls who come through and with really impressive resumes that eventually land an exec position.
This sort of bias is only seen in Old Row houses though, obviously because they have strong Southern roots.