The good news is that it's PVC trim so you shouldn't experience any rot issues.
The bad news is that's it's PVC trim so paint doesn't adhere to it easily.
Properly, the trim should have been:
Washed: by hand or light pressure-washing
Scoured with 220 grit sandpaper so that paint can better adhere to it
I believe the same effect can be achieved by ...
Sand rusted areas and apply rust primer to exposed areas (oil based, spray can)
Fine sand rest of door
Fill door indents with automotive 2 compound filler, sand smooth
Paint entire door with exterior latex & foam roll or spray can
Sand jamb, fill with same automotive filler or wood filler or leave it. Apply exterior latex paint.
You can put them roughly where you have marked them. You can get probably 1/4" eye bolts about 3" long, preferably stainless. Behind the trim on the corners 1 & 3 are at least 2x4 used in framing and #2 has a rafter close to that point, you will probably need a stud finder to locate it. These would be available at your favorite box store. ...