Your first question is utterly undefined in the rules. I have searched high and low for an answer to that question, and it just does not exist. Any time one move action involves different movement modes (and thus different speeds), how much you can actually move is just one big question mark.
The most “fair” thing is to pro-rate your movement speeds (e.g. you move 10 ft. with your 30-ft. land speed, that’s ⅓, so you have ⅔ of your movement left, so you can fly 40 ft. with your 60-ft. fly speed), but that would be massively tedious to calculate on the fly. This example used nice, neatly-divisible numbers; other situations easily might not (including yours).
I have not come up with a good answer for this, and mostly just try to pretend the problem doesn’t exist. When it comes up, I mostly just eyeball it and call it something reasonable, rounding in the PCs’ favor if necessary. It doesn’t actually come up that often.
For your second question, I would rule that a free action (not a 5-ft. step, which is a free action but can only happen once per turn and prevents other forms of movement), but I do not believe the rules cover that, either. Easier to rule on, though.
Basically, the rules seem to constantly assume that everyone will always use one single type of movement mode for all time, and that’s the end of it. They never address transitioning.