Only a few state have estate tax. If you are not in one of them, you owe no taxes on an inheritance. Any taxes owed would be paid by his estate BEFORE disbursement of funds.
The gift tax would be HIS to pay, though it's unlikely he would actually owe anything unless he goes over $5 MILLION for his lifetime. The gift is not taxable income to you. So either way, the tax burden to YOU is nothing.
They can't fight a legal will, so if you go that route, just make sure it's all legit.
If we are just talking about straight cash, it wouldn't be taxed if transferred after his death, so you should be fine. Make sure to get a third party verified will (with a lawyer), because the family is going to fight this one. They don't have anything to say about the life insurance, but the cash will be contested for sure.
Make certain that you are the executor (executrix) listed on the will, otherwise they will take their sweet time in dispersing those funds.
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