Don't know about if you need to do a gift tax for 2014 for her but probably not.  But when you sold it your cost basis is what she paid for it plus any improvements.  You do not get a step up in value when she died.  So you need to find out what her cost was, what she paid for it.

That's a problem.  Parents think they are doing the right thing by giving the house to the child but it's usually not.  Now your cost basis is what she paid and since you didn't inherit it you don't get the value on date of death.

What happens if I cannot get paper proof of what she had spent to build it and add to it over the 8 years she had the house, but only for the original price of the land and for the value of the "gift" as it is written into the legal paperwork. And I have a good guess-timate based on our past conversations. Also, finding these records in the rural areas of Hungary would be next to impossible.

What your mother paid for the house originally will be recorded at the county clerk's office. Usually it's filed with the original deed and construction permits and the such. SO if the recording office doesn't have what you need, the permitting office should.
If that house was at any time a rental, or if a home office was claimed any time during her ownership, then find the tax return with that info on it. It will have what you need for helping you establish the cost basis.
You can also check with the lender who provided the original construction loan and see if you can get the amount of that loan. The amount of that loan along with the appraised value of the land at the time of that loan could then be used to establish an original cost basis. I'm sure the bank required a land appraisal as part of that original loan, and that appraisal will be with the loan paperwork. I would expect the lender to change you a small "research fee" to go dig that information up for you. But you may be able to include those fees in your deductible sales expenses. (Not sure if you can or not really)

" ... rural areas of Hungary ..." implies you should consider paying for advice of someone experienced in US/Hungarian tax issues. Can be difficult with Eastern Europe ,,,

I already checked in Hungary for the taxes and legalities about this, it is much simpler and taken care of almost automatically. That is why I'm only concerned with the US end of it. I'll try to get ahold of a clerk's office in the village. The bank loan route wouldn't work... She sold her house here in CA and took the cash to Hungary when retiring and building the house on the parcel of land she purchased, all using cash (she always hated owing anything to anybody), she even paid off her 30 year mortgage here in just 22 years. I'm just frustrated about the gifting of the house. She thought it would make my life easier than letting it be inherited. That's why the value of the gift (house) was stipulated in the paperwork.

The value of the gift at the time of the gift does not matter for US tax purposes. What matters is the cost that she originally paid, plus the cost of any improvements that she made. If you can't to document this, you will have to estimate on your tax return. But, if you were audited, the IRS will only give you whatever basis you can prove.

Thank you, this does make perfect sense. Now I'm certain I cannot prove the cost of the house she built in 2007 that she gifted to me in 2014, because in Hungary, these records are only required to be kept for up to 5 years, and she used no loans to build it with. So, even though it was sold for significantly less than what she put into it plus I am forfeiting a tax deduction on the loss, I will be at the mercy of the IRS; it was at least a 40% loss (we calculated this when advertising the home), since it's too far from any major city. This is a misfortune, but what can I do...

If you have a loss, then you will have no US taxes to worry about. For personal use homes, losses are not deductible, but gains are taxable. As long as the amount of sale meets or exceeds her basis at gifting, there was no taxable gain.

She was in the hospital, most of the time, and I'm sure the last thing on her mind (and mine) was to file a gift tax return in 2015 for the gift in 2014. So, I'm fairly certain, there was never any filed. I did not realize there is such a thing until recently (after the sale of the house). Do I need to file one retroactively now, and do I file it in her name or mine?

@Rainman12 "As long as the amount of sale meets or exceeds her basis at gifting, there was no taxable gain."
You're backwards. Please delete my comment after correcting yours. 🙂

@sandorbatyi was your mother a United States person for tax purposes in the year that she made the gift? If she was a United States person  (a citizen or resident alien) then she would need to file a gift tax return to report the gift of the house. And you could do that now as the administrator of her estate.   But if she was not a US person, then she would have no obligation to report a gift to the IRS.  

Is there property tax in Hungary and is it calculated on the value of the property? If so, the tax records in 2007 or 2008  might be a good estimate of the value when new.

Yes she was a US citizen. She had no tax obligations for the home in Hungary. She paid no taxes on her social security to US either... it was the only income she had. The home was paid in full from the retirement money she moved back there with. The home was the only thing "gifted" to me while she continued to live in it until the very end. Home was valued at $150K and her staying in the home while it was in my name were both specified in the gifting papers.

Was there a deed filed with the court, or whoever records property deeds in Hungary? Do you have a way of getting a copy of the deed?  

In the US, certain deed forms when  a home is transferred to a child but the parent retains the right to live in the home have special tax treatment when the parent passes away, which may affect the taxability of the sale. It would be very helpful if you had a copy of the deed.

Yes, that is what I've been calling the gift paper. In Hungary it's just one paper done by an attorney and filed by her. It states that my mom will continue to live in the home until her passing, but its ownership is transferred to me immediately. It also states the value of the property that she is giving to me (approximately $135,000 at today's currency rates).