2 - Is it really infidelity? She'd thrown Peter out. While she hadn't and still hasn't divorced him, they were separated, not living together and barely speaking at the time. I wouldn't count that as an infidelity, especially after what Peter did.
As for the kids living with Grandma - I somehow don't think that's going to happen. Remember Zach playing Grandma off against Alicia? He know's she's a racist old bigot. He also put two and two together about Jackie trying to go through Alicia's computer but accidentally videoing herself instead Peter might want to live with her, but not sure about those kids.
I somehow think they'll end up staying in the condo with Alicia.