Question: Since they had friends why couldn't the Stivics move in with them so they wouldn't have to put up with Archie?
Answer: Yes, Gloria and Michael have friends, but when they got married they decided it was best to live *rent free* with Edith and Archie, while Mike was going to college. Living with friends rent free, for quite a few years, is not an easy thing no matter how close the friends are with them. Since the Stivics needed their money to pay for the tuition and its other costs, their living arrangement made it all easier to deal with. Hence the Archie and Mike scenarios.
Answer: In the show, he was already a Lieutenant. A promotion would put him in the next rank up, which for the L.A.P.D. would be Captain. However, some of a Captain's duties would be overseeing other officers and ensuring they're compliant with policies, regulations, and standards. It would also most likely take him out of the field. This is something Columbo has no desire for as he rarely goes to police HQ's. Nor does he show interest in compliance and standards (for example, not going to his semi-annual evaluation at the firing range). However, he could still be assigned to a higher pay grade based on expertise, which is a form of promotion that does not include rank advancement. This would be going from Lieutenant I to Lieutenant II. I don't believe in the show it's ever started what his pay grade is. Although, in s02e01 (I believe) he mentions making $11K a year. Whether or not this was a true statement on his part, if you could find pay scale information for an LAPD Lieutenant in the 70's, it could give you an idea of his pay grade.
Bishop73