The rear lip thing is just trim associated with the impact bumper. Can just be unbolted.
Weird piece on the front - again, impact bumper associated. Just remove and bin.
280Z rear bumpers don't need holes at the sides due to being mounted on hydraulic rams. Hence the lack of escutcheons/recesses for the bumper sides as per 240Zs, etc. You can buy conversion brackets to mount the 240Z bumpers on the rear valance - you will need to drill holes on the lower rear quarter panels for the mounting brackets on the bumper end sections.
It's a runner, it's registered, it needs improvement on-the-go, including a (maybe partial) paint job at some point. Someone will grab it, probably for a bit less than asking and have a decent, solid mobile project car.
As for the filler comment - your eyes are obviously better than mine! Nothing screams heavy filler, nothing more than you'd use with a basic repaint anyway. Of course, there's likely to be some somewhere, but I don't see a car "full of filler".
If I was in the market (with Dixie dragging on and ongoing Celica upgrades, I'm definitely not!), I'd probably nip over to take a look.