I'm a plus one on the suggestions to:
Use heat to smooth out wrinkles. Or stretch ensolite a bit to glue down.
The caulk to fix the tears. And getting a piece from under a bench or inside closet or cabinet to patch with.
What appears to be a crack at the door frame needs to be fixed. You can gently separate and peel up the ensolite with a plastic putty knife. Fold it back to make the repair. Glue ensolite back when done, maybe caulk, or patch if you cant get ensolite edges back together.
Using a plastic putty knife also how you would get material from hidden locations for patching loose. One suggestion when patching get a piece slightly larger than the patch needs to be and cut through patch material and into wall material. Then carefully remove the cut wall material. By cutting through patch material you know the patch will be an exact match for the cut made in the wall material. End up with a seam no wider than a razor knife cut.
3M spray adhesive seems to work well to glue ensolite to the walls, spray both surfaces, let tack up for a few minutes and stick. Specific directions on can and widely available.
I had good results cleaning ensolite with LA Totally Awesome spray cleaner a scrub brush and rags and bucket to rinse with. Went from dingy yellow and sticky to white. Really tough stuff that tends to clean up well. If your thinking of painting
you will need to clean well anyway but you may find it cleans up well enough that you won't need to paint
or at least looks nice until you do paint.
I think I have seen the plastic pieces that snap in at the seams for sale
but it was awhile ago, believe it was manufacturer doing a run to support the older models. If nothing else you can purchase "seam tape" which is thin high density white foam adhesive tape to cover the seams. It's the approach used by scamp
with ensolite wall. Or of course caulking them is also an option.
You really need that foam or some other insulation on the walls to prevent condensation.