Firstly are you sure its made from polyethylene and not polypropylene or ABS or some other plastic?
If it is PE is it (low) LDPE or (high) HDPE? this makes a difference in repairing as I think you can repair HDPE with LDPE but not vice versa.
You will need to try and make a "V" shaped groove in the cracks with a dremel or similar. When done Make sure everything is clean and grease free ready for welding together.
You will need a heat gun or a small blow torch and some plastic welding rods of the right material LDPE or HDPE you can get these easily on Ebay.
Then its just a matter of gently heating up the material and the rod and "welding" them together along the cracks.You will probably need to smooth out your weld as you go so just use something like an old spoon.
When you're done welding just give it a good rub down till its flat and any rough or low bits you can fill with plastic filler that you can get for plastic bumpers and finish that with sanding until it's all smooth. Make sure the plastic filler is suitable for PE though as some aren't.
Looking at your bodyshell it looks like the cracked area may bend/flex when pressed on, if that's the case I would look to brace up the inside with a frame of some kind to stop any flexing before repairing it as your new welds won't be as strong as the original material.
As for painting PE it's really hard to get paint to stick to it, at minimum you'll need to sand and prep the whole bodyshell as you would a normal car then prime with some adhesion promoter then plastic primer then a suitable top coat. 2 pack paint might work but it's nasty stuff if you don't have the right PPE gear. Even then I wouldn't guarantee that it would stick.
Try looking on boat/sailing or canoeing forums for advice as PE is used to make kayaks etc. Your shell looks to be made of fairly flat panels so you could try to vinyl wrap it maybe, probably be no more expensive than painting it and no sanding down or nasty paint fumes either.
Hope that helps and good luck !
