Hi.
I run a Sprite Pop-Top from that era, which I have renovated and remodelled into unit to precisely match our needs.
Many spares are "generic" - so you do not need to get a specifically Sprite part.
For the skylight, measure the dimensions of the hole and find one to fit. It is possible to change the size of the hole, though with very great caution. Modern skylights can come with mosquito screens and/or blinds, so would be a worthwhile upgrade anyway.
As for the rear lights, I imagine, like mine, they are nothing fancy, just stuck on the outside. Just go to Halfords and buy new ones, a little bit bigger than the old ones.
I have bought most of my spares off ebay, and saved a fortune, but it is up to you if you are confident and have the patience to wait for a bargain.
The battery you want is a leisure battery, not a car battery, of 100Amp Hours or more. Worth shopping around for, as prices vary wildly.
Noseweight is trickier on old vans. Start with the car's limit as your maximum, but the caravan limit may be very dificult to find. It is almost certainly not marked on the van, and the net has little info available. Personally I aim for 70Kg, and it seems to tow nicely at that, but I can't make a recommendation for you!
An advance word of warning. Teh brake adjuster screw is almost certainly rusted solid, and you will have to strip the mechanism to free it. Before you do so, take a photo of the assembled system - on BOTH wheels - or you will spend forever trying to work out wich spring goes where.