1. Basis is a different prospect, if you mentioned that before, I didn't see it. It's not clear to me if the owner gets a basis adjustment if a non-owner pays for the improvement (it could be any improvement). I tend to think the owner does not get a basis adjustment, but I leave room to be open to be persuaded otherwise.
https://www.irs.gov/publications/p551
In the case of joint property, let's say a home with cost basis $100,000 and 3 equal co-owners and 1 owner pays fully for a $10K solar system, I think the first owner's basis is $43,333 and the other 2 owners retain their $33,333 basis. But I'm not confident without doing more research. (And the basis is reduced by any credits, of course.)
2. Yes, if you are a resident in a home and you fully pay for the system, you are the only person who can claim the credit and you can claim it all.
3. Each piece of property (hot water heater, solar panel, etc.) is claimed as of the date it is placed in service (installed and turned on), regardless of when the contract is signed or the property is paid for, using the tax laws in place at the time. You can't claim the same property more than once, but you could claim solar in 2 different years if, for example, you installed solar panels on your house in 2022 and then you installed more panels on your detached garage in 2023, both would qualify on the corresponding year's tax return. So if you install different qualifying items in different years, you can claim a credit on each return for that year's qualifying property.
However, I don't see any qualification for a geothermal heat pump water heater. Section 25C allows a credit for a natural gas or electric heat pump water heater. Section 25D allows a credit for qualified geothermal heat pump property, but the term “qualified geothermal heat pump property” means "any equipment which— (i) uses the ground or ground water as a thermal energy source to heat the dwelling unit..."
https://www.law.cornell.edu/uscode/text/26/25C
https://www.law.cornell.edu/uscode/text/26/25D
If I am reading that correctly, if by hot water heater you mean it is used for hydronic heating (hot water circulating in pipes to warm the house, or cool water to cool the house) then you qualify, but if you mean it is used to heat potable water for drinking, cooking, washing and bathing, then it does not qualify because it does not heat or cool the dwelling unit.
4. To deduct mortgage interest you must be a debtor on the mortgage, and be an owner of the property, and actually pay the mortgage. To deduct property taxes, you must be an owner of the property, and actually pay the taxes. You can deduct what you actually pay.
(For a technical explanation, as long as you are one of the borrowers on the mortgage, and one of the property owners, you have joint and several liability for the taxes and interest, meaning the taxes and interest are equally due from all owners, and the lender or county can collect from whomever is most convenient, if you all don't pay. You're not paying "someone else's" bills, they are 100% everyone's bills.)
