You have to work that out with whomever you own the home with. The town gives a figure of what they want for taxes and if they don’t get it they file a lien on the house. They could care less who owns the house. All they care about is collecting their tax.

Yes, you may claim the taxes you paid as long as your name is on the trust deed. You may not claim any interest benefit as you have no liability.

Either of you can claim the portion of both the real estate tax and mortgage interest that you individually paid.

Who paid the tax? if you did or paid 1/2 then declare what you paid