I'm not going to even try with the 1041, as my knowledge of the rules for that is just to limited.
But for you on your personal 1040 tax return, the cost basis of the property is whatever the FMV of the property was on the date of the original owner's passing. Then using that new cost basis, depreciation starts over from year 1.
Typically, the "in service" date for you would be the date the property was titled to your name. But that's not a hard fast rule as I understand it. I could be the date you actually started collecting the rent in your name, even if before the property was actually titled to you.
I also understand that all prior depreciation taken by the original owner, "evaporates" upon their passing, with no exceptions I'm aware of.
Now I can't speak for the 1041, but for the deceased final 1040, you don't report a sale, because no sale took place. For each asset as you work it through the assets/depreciation section, you select YES on the "Special Handling Required?" screen. That will "dispose" of the property as of whatever date you specify, and will not ask for any sales information; as it shouldn't since nothing was actually sold.
Things might be different since the property passed to an estate before it was passed to you.
