Last - I don't take passengers I don't know and trust my life on, wouldn't be the first suicide from the right seat
Happily, as a PPL, it can be presumed that you're only taking people whom you have invited, and thus you know - or else, how did they get invited? If you know someone whom you suspect is unbalanced, you should be doing something for them other than taking them flying! I can't say that no one has ever committed suicide from the right seat, but I think the chance that you might choose ti invite a person along, who then seized upon the opportunity to wrestle control away from you long enough to crash the plane are infinitesimally small - worry about absolutely everything else before that!
As for passengers being sick, firstly never coax a person into flying, if they choose not to accept your invitation, smile understandingly. Not everyone is meant to fly, and some know it. Once airborne, it is your job to take enough interest in your passengers to be aware if they have stopped talking, that will be the first sign they are feeling unwell. Ask them how they are feeling. If they say "fine", they could still be attempting to conceal airsickness, make the flight smooth with fewer turns, and consider ending it early. If they say they are feeling unwell, certainly fly smooth with few turns, and end early. Direct their attention to features on the horizon, and fly so they remain in view as much as possible. When you need to turn, direct their attention to a feature which come more into view as you turn, not something they'll have to twist or look down to continue to see. In 45 years of flying hundreds of people, often on their first flight, I've only had three be airsick, and two of those were entirely mu fault for maneuvering when I should have flown much more sublimely. More commonly, I have quietly terminated a flight early, suspecting a passenger was feeling unwell, to have them continue to assert that they were fine. Memorably, in the case of one person, who was my passenger in her professional capacity as an aircraft engineer, I have, on three different flights brought her back early, as she was so quiet, and hardly responded to me, that I figured she was unwell. She keeps telling me that she loves going flying. I have told her twice now, that she should assert that to me while flying, rather than after I have landed, and I'll give her a longer flight!
Just because you might fly a four seat plane, does not mean you have to fill the seats, just take one person, until you're used to carrying passengers.
A reason to not take kids in the front seat might be that kid in the front, and parent(s) in the back is poor C of G, but more importantly, see point above.
I once had a teenage passenger front seat with me. I knew that this person was mentally disadvantaged, so was not entirely sure what to expect. He seemed to be having a wonderful time, and I let him fly just a little at altitude. Later in the flight, he decided that he'd like to fly again, and did not accept my instruction to let go. So I pitched the plane up against his control inputs, and released his seat lock, so the seat rolled back while I then pushed the control wheel forward. It was momentarily messy, but he could then no longer reach the controls. If you're really uncertain about passenger and controls, position their seat out of reach. But, if you're uncertain anyway, you should not take them at all.
Sure, confirm insurance. But, if you're renting the plane from a reputable organization you can be confident that it is correctly insured, it's a legal requirement - but sure, ask. I have been asked several times to present my papers during random ramp checks, so it never hurts to have them in order! Ironically, one of those ramp checks was at a dock in Arctic Canada, while I was flying (solo) a Transport Canada flight test. The two Transport Canada inspectors were un moved when I explained the purpose of the flight, show us your papers.... Well, I was insured to fly the plane under my employer's fleet insurance, for which I was not carrying any papers (my oversight). he plane was insured, and those papers were there. Happily for me, the inspectors did not figure out that I was not covered by that policy, and accepted what I presented.
As said, as a PPL, your only reason for taking a passenger is for fun, so make it fun, and keep it fun.