Regarding Arizona's resign-to-run laws:
If I'm reading the "Note:" section right, Gallego can announce a run and not violate the resign-to-run laws so long as he doesn't actually file until after January 3, 2020 (or, if he falters before then, drop back into his safe House seat). How he would do that and still get people to donate money to his officially non-existent campaign I don't know, but there you go.
Alternatively, he could just do what McSally did and wait until after the January 3rd deadline.
Resign to run doesn’t affect federal office holders.
And you can't run for both the U.S. House and another office simultaneously in any case.