Sure.
You can buy it from the owner.
Sure.
You can buy it from the owner.
You have no rights to the house just because you've been renting or sorta renting just because the owner hasn't paid taxes and/or the mortgage. It's a fallacy that renters have rights to the rent money just because it isn't remitted to the bank. The business of renting is more involved than just apportioning the rent payments to the bank.
Until either the bank or the tax man takes action against the house, the only way you'll get ownership of the house is if you arrange to buy it from the owner. Of course, the owner will either need to satisfy the bank/tax obligation or you're going to take the property subject to all his debt.
You paying the money to someone other than the landlord means you are in breech of the lease and you could be evicted. You're throwing away your money.
It is highly unusual that property taxes can go unpaid for 6 years without the county or the township taking action for a tax sale or tax foreclosure.
You could potentially acquire the property through a tax foreclosure. Read up on the procedures here.
In some cases, the mortgage lien can be cancelled.