I agree with Jack; it appears that he has transferred to you the property reserving a life estate for himself. That's another approach in estate planning that is popular some states.
The life estate means he reserves for himself the right to live there, rent it out, etc., and also continues to bear the costs of the property maintenance, etc. Basically, he treats like his own home with the exception that he cannot sell it nor can he get a mortgage loan on the property. Furthermore, any liens that arise from his debts AFTER the grant of the life estate will not attach to the property, but any liens that arise for your debts would attach to the property.
You are not required to sign the deed. Only the seller/transferor must sign it to be effective. You do, however want to ensure that the deed is properly recorded.
As for the tax treatment, the creation of a life estate is not treated as a gift at the time it is created because he's retaining nearly all the rights of an owner of the property. For that same reason, the value of the home is includible in his gross estate for federal estate tax purposes. With the estate and gift tax credit being so high right now he doesn't have any worry about estate tax right now. That might change in 2026 depending on what Congress does when the 2017 tax act expires. I don't expect it will go any lower than what it would have been had the 2017 changes not been made, which would still exclude more than $5 million of assets from the estate. If his assets aren't close to that it's likely that the inclusion of the home in his gross estate will result in any estate tax to pay. On the income tax side of things you get the benefit that your adjusted basis in the property will become the fair market value of the property on the day he dies, wiping out all the gain that occurred while he was alive. That means if you decide to sell it shortly after he dies you'll little or no income tax to pay on that sale. This combination of an estate below the value to trigger estate but giving you the basis step up is what makes it a good estate planning option. There are other ways to achieve the same thing and evidently the attorney and your dad agreed this route would best suit what he wants to achieve. For you, this arrangement works out well.
So the bottom line is that the attorney is not doing anything unusual here, at least with what I know of what the deed says from the piece you quoted. I'd always want to read the whole thing to make sure it's going to work as it's supposed to. It appears that you've pretty much accomplished what you wanted by nudging him to see the attorney so there shouldn't be a need to pressure him further regarding the house. That's taken care of.