Patches are permanent if you used the vulcanzing-fluid type. The patch is fuzed onto the tube and trying to peel it off will result in ripping the tube. However, there are factors that may result in a less-than-ideal patching job, such as inadequate scuffing of the surface down to bare rubber. Or taking too long to apply the vulcanzing fluid, resulting in areas with differing adhesion. Or applying in uneven amounts. I prefer to apply a popcorn-kernel size drop to the patch and use the patch itself to smear the fluid onto the tube. This results in the fluid being applied to the entire surface simultaneously and in a very even layer.
As for mounting the tyre, here's a technique that'll work consistently well to avoid pinched flats:
1. with tyre & tube off the wheel, give the tube a little pump so that it's round, but just barely.
2. insert tube into tyre and lay over rim.
3. insert valve-stem into rim and push one bead completely over rim
4. stuff tube completely into tyre & rim so that remaining bead sits flush on rim-edge
5. start pushing over the remaining bead by hand
6. that last 6-8" will be tough, DO NOT try to push up on the tyre at the middle of the unseated section, no human is strong enough to stretch the bead on a tyre.
7. instead, push SIDEWAYS on the tyre at one of the two spots that wraps up and over the rim-edge; you don't need to stretch the bead this way, just push it sideways.
8. The last bit 3-4" may need tyre levers, to do this cleanly, the tyre lever must never leave contact with the rim.
9. place the tip of the tyre-lever on the rim-edge just under the unseated bead.
10. GENTLY push it up under the tyre, BUT don't push it further than the top edge of the rim, you can feel it drop down slightly. Again, don't lose contact with the rim, this ensures that you never open up a gap between the lever and rim into which the tube and squeeze into and get pinched.
11. next slide the tyre-lever sideways as far over as possible towards the area where the bead goes over the rim-edge; use your other hand to pinch the tyre onto the rim so that tyre doesn't slide off
12. then GENTLY lift up the lever and push the tyre sideways; typically you don't need to raise the lever more than 90-degrees perpendicular/sideways relative to the rim
13. pull lever out and repeat for other side. Remember, constant contact between the lever and the rim and don't poke the tip much further than the edge of the rim
14. After the entire bead's on, let out some air from the tube and pull the tyre sideways to inspect the gap between the rim-edge and tyre; no tube must show. Move over 6" and push the tyre sideways again and inspect for tube. Work your way around the entire tyre on BOTH sides.
15. only after you've inspected the entire bead on both sides, then you can pump it up.