It is much simpler than you are making it sound.
Lets start with a quick note about when you have to make the checks from the fly skill text:
Note that these restrictions only apply to movement taken during your
current turn. At the beginning of the next turn, you can move in a
different direction than you did the previous turn without making a
Now while making your movement during the current round, no extra squares are moved into. If you want to do anything but continue to move straight once you have started, you make a check, and if you succeed, you are now facing the new direction. Performing one of these maneuvers does not cause you to leave your current square.
Is the 90° turn literally like moving up a square then turning right
or left a square?
No, you never leave your current square. Just change orientation.
If so, is the 180° a U turn perhaps, move forward 1 square, then to a
side, then back in the direction you came, putting you in the square
next to where you started?
again you never leave your current square. Just change orientation.
According to RAW would a 180° turn be possible as you ascend? Such as
moving forward 1 square, up one square, then back in the direction you
came, but now at a higher altitude, thus being over the starting
Yea, you can rise at 45° angle at half speed without a check. (moving forward and up one square). Then do a check to perform a 180° turn. Then move back one square in the direction you started.