1) If he's wizened enough to lead his people, then yes, he would be considered a patriarch. Alley Oop was already one of the leaders in his cave man tribe until he was introduced to the future via time machine.
2) Sgt. Snorkel gets a bonus (as do most sergeants) if they get their men to re-enlist. Beetle is always goofing off, but still gets a paycheck, if he went civilian, he'd have to find a job.
3) Probably custom made for him at a shop.
4) Fritzi Ritz was originally a flapper, then with the introduction of her niece (Nancy), she moved on to become a actress. She had boyfriends in the past, but chose to focus on her film career.
5) Because he's Popeye's sidekick, and in case of a situation, he serves as a distraction or bait for the enemy.
6) They think it's normal for a kid to be living in his own dream world, as young children tend to do.
7) There has always been a Phantom (since the 1500's) to fight against the evils that would take advantage of the local tribes. The legacy is passed on from Father to Son giving him the appearance of being immortal. He is part of local tribal folklore as well as a hero to those tribes.
8) Without the cat there wouldn't be a comic strip. However despite their knocking heads, they both like each other and share a love of certain things. As with any cat household, it's a symbiotic relationship. ("If you feed today, I won't kill you in your sleep tonight")