Here are some thoughts about your list - my notes are below each item with some rough costs for parts. Try not to be discouraged - this is a lovely trailer but it will need some work to restore it to it's former self. Focus on the systems save the cosmetic stuff for later.
1. Toilet- bowl
This may be your biggest challenge. If the original toilet is still there you may have a heck of a time rebuilding it. In mine
I found that some sealand parts were interchangeable BUT replacing would be the fastest path forward and what I ultimately did after two rebuilds. $300.00
2. Hot water heater-
Replace - new ones are efficient and the entire unit simply slides in. $400.00
3. Water tank under the bed
Replace - make sure that you get a thick walled water tank - many are thin and will not survive long. Vintage trailer supply is your best bet. $300.00
4. Pump is not hooked up its very old prob need new one.
New pump $200.00
5. Sink in bathroom - repair
6. Battery is shot - 2 new batteries AND an intellipower converter to replace the old univolt (which will trash your nice new batteries if it's still working).
2 Batteries and $200.00 for univolt redo.
7. stove, burner tops fridge sink- need to replace the faucet on sink
Leave for now.
8 underbelly is solid no corrosion rust damages panels etc
Buy some rivets - you will need them to get belly pan back in place after various repairs. $40.00
9. grey water and black water tanks -
Unless the trailer was retro fitted, there is no gray tank. One can be added however and there are several ways to do this either under the floor of in the floor of a closet (which we did). The black tank will need to be tested - might still be good. Cheap alternative for gray tank is a blue tote (portable tank) but this gets old quickly... $80 - $300.00
10. Windows on camper are sealed but horribly
NO Silicon on aluminum. You can remove and reseal as time permits
11.. furnace has never been turned on looks scary
replace - safety concerns. $400.
12. heater on side of fridge is working but needs a safety once over please
Addition: Co2 detector. $50.00
13. panel under hot water heater on outside of airstream is loose
These old panels rattle - may be fine. If you replace hot water heater, it will come with a new cover.
14. inside the trailer the skylight in the back has an issue with the fan setup its a mess cover is wrong etc.
Replace fan/s with fantastic fans - $150.00 each
15. inside the front- skylight over the couch
There are after market covers and new lifters available for this but the cheapest path forward and maybe the best solution is to go to a window shop and get a fixed, skylight cover. There are plenty of windows and ventilation in this trailer - the skylight doesn't really need to open.
16. lights all work need new bulbs in all lights and fixtures by couch.
Bulbs from auto parts store. $10.00
Cosmetic - safe for another date
18. Propane lamp
This is a humphrey Lamp. Parts are available and inexpensive.
19. fan over stove not operable
These can be taken apart and fixed but you can replace if needed. I never use mine.
20- Braking system/propane tank check/ running lights etc-
21,. left side tire losing air
New tires. $700.00
new axles - yours appear to be shot. $2000.00
22. (I added this) Replumb with Pex. You have a lot going on with the plumbing in this trailer - take the opportunity to replace old copper lines (which may have winter damage) with flexible pex lines.