why can't black just put a stone in upper left corner? Then white would lose one point.
It does not work this way. In territory scoring, the captured stone counts for a point (which offsets the point for a stone played in one's own territory), and then the intersection is freed up (undoing the supposed damage to territory of placing it). In area scoring (which I strongly recommend for beginners - it's also faster to count on 9x9) it's simply obvious: the borders of the area haven't changed, therefore the covered area of the group hasn't changed.
Territory scoring (and counting) is in essence used as a shortcut. The idea is that territory represents points where you could later put a stone at your leisure and count it towards your area, but your opponent cannot - because such a stone is doomed to eventual capture. These facts are inherent to the definition of territory; if you can't put the stone there, or your opponent can, it is not your territory. (Notwithstanding, of course, the last two open spaces required to prevent a group from dying to self-atari. Some historical variants of go did not count points for that; this is called a "group tax". And yes, board positions involving a seki do make this more complicated, but not irreconcilable.)
So, in territory counting, you count a point for each intersection of your territory, because it represents potential area that can't be taken away from you. (In area counting, the players just fill it in during the counting phase.) You also count a point for each capture, because it represents area that your opponent had, but you then removed. (If you kill a group, for example, that changes the points involved from "will be covered by the opponent at the end" to "will be covered by you at the end"; so it effectively counts double.) By doing this, you get essentially the same result as with the area rules.
In some rare situations it can cause a point or so of difference in the overall score, but it does not create the kind of difference that beginners commonly imagine. AGA rules, with the use of "pass stones", are designed to ensure that territory counting gives the same result that the area scoring rule dictates.
Or white would have to capture it and get a point instead, but then there would be three white stones within the area and that would mean again for white to lose three points.
It does not work this way either. The idea is that the players are taking turns; while the opponent is capturing your stone, you would be filling your own territory. Or, more shrewdly, passing - but that is exactly why the AGA rules use pass stones: so that it costs you a point either way.
In beginner games, it's common that the players aren't sure whether some invasion could live. Please feel free to play it out. As you and your opponents get stronger, increasingly more complex situations will become increasingly more clear. You can worry about whether you are insulting your opponents by trying nonsense, when you reach a level where you know (and expect your opponents to know) that it's nonsense.
In some rare situations called semedori, it can happen that playing inside opponent's territory (especially at a cutting point) can end up being worth a point (or more) - because there is some tactical threat that eventually requires multiple plays inside the territory (while opponent applies pressure from outside). For this to make a difference, the initial play needs to force at least three eventual inside moves: one to balance out the thrown-in stone that will be captured, one to balance out the move that was already owed to protect against the semedori threat, and a third to make net profit above that breaking-even.