I've been evangelising this to people around me and I feel like I should evangelise it here to you comrades too - dwarf citrus trees are really fucking cool. For those who aren't aware, these are regular citrus trees of whatever varieties (lemon and lime are the most common) that are grafted onto dwarf rootstock so that you get full sized fruit out of a tree that stays fairly small, so those of us without a garden can grow them in a pot on the balcony. They're suuuuper easy to grow, they're hard to kill, they give you delicious fruit, they're really good looking trees even when they're not fruiting or flowering, and extra cool looking when they are. I reckon having cool plants that you can watch grow over the months and years is great for mental health, and it's twice as good when you can also watch fruit grow, and then use that fruit in your cooking and/or fancy alcohol.
I grow a bunch of veggies too and they're great and all, but they're seasonal and more work and constantly in the process of dying from something or other, but my citrus trees have been hardy as hell. They need a bit of sun (mine don't grow at all in winter when my balcony doesn't get direct sun), and they might not stand up well if you have freezing winters (though I've heard of people keeping them inside in the winter). Otherwise just water them deeply every few days and fertilise them every now and then (a bit more in summer, a bit less in winter).
They're not that expensive - in Australia they're 30-50 dollars (which I guess is about 20-40 freedom moneys), plus the cost of a couple of bags of potting mix, a pot (you can go fancy but a cheap plastic one will do, especially for the first couple of years), and a small tub of fertiliser. I can personally recommend Tahitian lime and Eureka lemon (plenty of people swear by Meyer lemon as well), and I've got a new kumquat tree growing now as well.
Anyway that's all I had to say, feel free to have a struggle session about the name "dwarf citrus" in the comments below.
I think it depends, they tend to go through phases of rapid new leaf/branch growth and phases of flowering/fruiting, and then mine seem to just sit there during winter. Some varieties produce fruit more or less all year, others have one or two fruitings per year. Depending on how big the one you get is, I think it might take a season of growth or you might start to get fruit pretty soon (though you won't get many in the first year). I just got a kumquat tree a couple of months ago and it already seems to be starting to bear fruit, even though it's still really small.