Correct probability calculation for Minesweeper
You get different probabilities because in each case you only consider a particular part of the board, and thus in each case you only consider only a strict part of all the information that is there. So, there really aren't any contradictions here.
If you want to know what the probability is given the whole board, then your calculations will become more complicated. In fact, you'd have to take into account even more than those three 'trajectories' you mentioned ... and if you add the information that there are exactly 10 more mines to place, it becomes more complicated yet.
Still, I would say that your third line of reasoning (that start with the 2 in the top right of the open region) probably gets closest to the actual probability, for the following reasons:
It takes into account the most information (indeed, it includes the information regarding the 5-square).
There is a good bit of room left at the top left, thus you can easily pack different numbers of mines there, so even knowing there are 10 mines left should minimally impact/constrain what could happen next to that 2.
The 3 flags stacked on top of each other next to the 5 naturally carve the space in a 'left' and 'right', and there is no direct line of reasoning as to how satisfying the numbers on the left will impact what happens on the right.
So, the number of ways you can work out having a mine directly to the left of the top right 2 should be very close to the number of ways you can have a mine below that ... meaning that I would agree that, even if you take into account the whole board, the probability of a mine in each of those squares is indeed around $1/2$, and with that, the probability of the top square next to the 4 being a mine is indeed very close to 3/4
In general, though, yeah, try and take into account everything as is 'humanly possible' ... which in most cases is not considering how many more mines there are. But the example you gave here does show how certain lines of reasoning take into account more information than others, and the more information you take into account, the closer you tend to get to the probability if you somehow could take into everything.