The problem with the kiosks at the MK is that they tend to come and go/open and close without warning. In addition to the ones you listed and the ones in City Hall, in the past there were also kiosks in Fantasyland near Philharmagic/Peter Pan and in a couple of locations in Tomorrowland. But just because those were open in the past doesn't mean they'll be open again in the future. Your best bet is MDE and the park maps when you're actually there.
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Do I have to wait until all 3 FP are used to get another, or if I use one, potentially I could get one more FP if I actually wanted to wait in line to get one more?
The explanation on MDE sounds like I might be able to do the second option.
That's true.
Although there IS another option. (Just be very sure that you want to do this.)
1. BEFORE you USE your first FP+, go on-line with the app or site (or to a FP+ kiosk) and CANCEL both of the other FP+ you have pre-booked.
2. Then, once you have used the remaining ("first") FP+,
you can immediately go to any FP+ kiosk and book another (so-called "4th") FP+.
It can be for any available FP+ attraction (including the one you just rode, if you like.)
3. After you use that "4th" FP+, you can book another ("5th") FP+ at a kiosk.
(And, so-forth.)