Yes, the MPS2222A and the PN2222A are essentially the same device. Here are the datasheets for them:
You can see that they have the same pin configuration, and all of the operational specs are virtually identical. When you see two devices with the same "root" number, in this case 2222A, it's a good bet that they're pretty much the same part from two different manufacturers. This happens a whole lot with discretes.
Q4, the ZTX450, has a few minor differences, but basically it's just rated for slightly higher power dissipation than the other two (1W, vs 625mW).
So yes, any of them will work.
Provided you don't exceed any of the ratings, pretty much all NPN transistors are freely interchangeable in simple switching applications. You could stick a 2n3055
in there and it'd work. Were we building audio amplifiers, then we'd care more about internal capacitance, gain, and so on. But in this application it doesn't matter in the least.