Yes. Parental influence would be tough to deny. Normally developing children use modeling (imitation) to instruct their behavior.

This is why kids like to pretend to play kitchen or use a broom. They see you do it.

Anecdotally, I have seen children who have ‘bad attitudes’ do a 180 when the parents make an effort to model calmness and positivity. Anxious, stressed out or negative emotions in parents affect the kids.

In most settings, mood is contagious and is set by the leader. The catch is you have to keep it up.

Yes, of course it does. Parents choose which school the children go to, for example.

Not just that: where you live, what kind of house, is there green space nearby, what toys are there, how many people are around in the house whether you spend a lot of time with friends/grandparents, whether there is a lot of interaction with the parent or they are just left by themselves or with the TV on.

I'd argue parental influence falls under genetics and environment, assuming your genes come from your parents.

I wonder if people who are more adept at creating and selective recall of memories tend to be happier individuals.