You need real legal advice and tax advice, not random strangers on the internet.
As regards your husband's tax situation, it is very important to know the exact form of the deed. If his mother has a life estate and your husband is a "remainder man", that means your husband can't sell the home as long as your MIL is alive. In that case, the IRS view is that he was not given anything of value and will inherit the full value of the home with a stepped-up cost basis when she dies.
If the deed was "in fee simple" and he is the owner without restriction, then his cost basis, whenever he sells, will be his mother's cost basis, and he will owe capital gains tax on the gain, unless he lives in the home as his main home for two years before selling it. (And it needs to be his real main home, not just someplace he changes his mailing address to while still living with you and the rest of the family.)
There are other types of deeds, those two are the easiest to explain. You would need to review the deed language and consult a tax specialist.
If he is the owner of the home, he needs to document his cost basis, which is his mother's adjusted cost basis. That will depend not only on the original purchase price, but also the fair market value on the date his father passed away, plus the cost of any permanent improvements. A real estate appraiser can document the 2015 value. If the home is in a community property state, the mother's cost basis was stepped up when her spouse died and is equal to the FMV on the date he died. If not in a community property state, half the mother's cost basis was stepped up and half is her original basis (plus any adjustments for improvements). Your husband needs to diligently establish each part of the cost basis and save the documents for as long as he owns the house plus 6 years after he sells. The more cost basis adjustments you can prove, the less the capital gains.
I also strongly suggest you see an elder law attorney, who can advise on the tax, financial and legal implications of this situation. If your mother-in-law requires full time residential care (covered by Medicaid) the home transfer in 2018 might be seen as a gift that results in penalties and problems with Medicaid. (There is a 5 year clawback on large gifts.)
1. Whatever the reason, your spouse now owns the home, and will be responsible for capital gains when he sells. The question is how much gain, which depends on the basis, which depends on the type of deed, the state where the house is located, and other factors I described above.
2. A tax return is required if there is taxable income more than the standard deduction. If there was not enough taxable income to require a return, a return did not need to be filed.
3. If your spouse moved into the home for 2 years after his mother dies, he would qualify for the exclusion of $250,000. It has to be his main home, he really has to live there, not just for show. If he uses the exclusion in this way, then he would not be able to use the exclusion again if you wanted to sell your combined home for at least 2 years after using it for the sale of his mother's home. You would have to decide if the 2 year disruption is worth the amount you would save, which depends on the amount of gain, which goes back to the deed, the basis, and so on.
4. You don't have anything to report on a 1040 until you (your husband) sells the home. Then it is reported as a capital transaction. How much gains tax you pay, if any, depends on the factors discussed above.
