Second, you really should get proper legal advice on the tax implications issue. There's no way anyone could answer those questions.
Third, assuming you're talking about property in Washington state, the sale should not affect the assessed value for real estate tax purposes, and being a closely related transaction it shouldn't even be evidence of value. If you're talking income tax basis, again I would refer you to a tax practitioner.
Finally, I would suggest you get your own counsel to assess the risks of taking this property. If this was say a meth house or had oil contamination, etc., the property could be a liability rather than an asset. There might be other risks.
But why a quit claim? Are there any existing or other encumbrances? I'd order a title report and check it closely. You will assume any loans, liens or defects in the title. If there are any loans, the lender must agree to the transfer or more likely accelerate the balance.
Tax implications depend on the nature of the transfer. My sense is that you will have
to pay taxes on the full value of the property., if you declare it.
But, if it's exchanged by quit claim, not sure how the IRS will know
But I'd be careful.
So the first issue is: Are you actually getting anything? I would work with a title company to make sure that you actually have good title and no encumbrances, before you invest any money in this transaction or in the house.
The second issue is: What are you getting? Are there mortgages, back taxes owed, city code violations, or other legal issues outstanding?
You don't say if this is a gift or a sale. If a sale, you should use a statutory warranty deed (and title insurance) to be sure you are getting what you're paying for.
If a gift, your friend may owe gift taxes. This potentially affects you because unpaid gift taxes become liens on the property transferred. Non-resident aliens may not have the same gift tax exclusions as everybody else, so gift taxes can kick in at much lower amounts.
The "assessed" value is what the local assessor values the property at for property tax purposes. In Washington, the assessment can change every year, and is unrelated to the "purchased value decades ago."
I think you mean what would the house be valued at for federal gift tax purposes. Check this with your accountant, but I think this is how it works:
It would be valued at current value for calculating the gift tax, but the basis going forward would be what your friend paid for it plus improvements plus any gift tax paid. So if your friend paid $100,000 for the house originally, but it's worth $150,000 when he transfers it to you, for gift tax purposes it's worth $150,000 but you receive it with a basis of $100,000, so if you were to turn around and sell it tomorrow for $150,000, you would also owe capital gains tax on your profit of $50,000.
You need a lawyer.