Even so-called self-pollinating fruit trees often do much better if there’s another fruit tree around they can cross-pollinate with. Unless it’s one of those with two varieties of apples grafted onto one trunk, in which case it can self-cross-pollinate.
The location makes a huge difference. We moved house 3 years ago, and transplanted our apple tree from its shaded and slightly domed (i.e. rain runs off) spot at the old house to a sunnier and slightly low (i.e. rain accumulates by its roots) spot at the new one. In its 10 or so years at the old house it had yielded maybe four apples. The first summer after moving it was basically just the roots recovering - I don’t think it even bloomed, but it didn’t loose any limbs. The second year we got around a hundred apples.
A lot of bud thinning after planting is about getting commercial orchards up to production. You don’t want to waste sending a crew out to tend and harvest under-formed and misshapen fruit; it’s best to put that energy into root development. For a potted hobby plant I can’t imagine it having any detrimental impact either way and the trees clearly aren’t suffering. I am bitterly jealous.
I’ve kept a dwarf lime tree in a pot for more than 20 years now. I bring it inside during frost season in NC, and it usually drops half or more of its leaves in protest. Come spring when I put it back out I get a bunch of new growth, blooms, and eventually 3-15 limes around the time I bring it inside again in Oct/Nov. It likes a little fertilizer and plenty of water in the summer.
Our Meyer lemon produces fruit year-round here in the Bay Area. Once it gets started there’s no turning it off.
Re Fuji Apples, it depends on the climate. Fujis need some 200-600 chill hours a year (depends on who you talk to) to produce, and it’s been a warm enough winter that I wouldn’t expect much this coming year. Our 30+year old apple tree with half a dozen different varieties grafted onto it is just putting out leaves now, and I predict we’ll get a meager harvest until we get cold winters again.