What do Sims learn from household Sims?

I'm afraid I do not understand at all. Do you mean skill mentoring? Character values? Known traits?

OP, I'm thinking perhaps English isn't your first language. I believe you meant despite, not spite, as they have two different meanings! But I'm uncertain just what you're trying to say, too. If you're talking about the kids in your Sims' household being taught Values and stuff, over time they will have their values increase. Sometimes, depending on the kid Sim's actions, they will decrease. Other than that, I'm lost. Sorry.

I’m not entirely sure what you mean but here’s what I think:

A way for your active Sim to teach other Sims a skill is by having the Mentor reward trait and level 10 of that specific skill.
As far as I understand social interactions such as “talk about gardening” does NOT skill up another sim.
However if they’re part of your active Sim’s club (Get Together) and they perform activities in a group e.g. gardening, all sims should get a gardening skill boost.

So when you invite those sims to move into the active household they should have some level of (in this case) gardening skill.

Is that what you’re trying to do?

There are a few interactions that should raise the target sim's skills a little: Enthuse about Juice fizzing and Share Vampire lore definitely do this. I'm not sure about most of the other skills, like talk about fitness or mixology. I think they don't do anything.