Single tax payer died owning a commercial buildling.

Can I just copy and assets over from his 1040 Schedule E and claim any depreciation on the 1041? His estate received rent and have expenses on this building. There will be a Schedule E and F on his 1041. My understanding is the income retains its character.

Form 706
This same taxpayer has a check coming from US AG dept for some gov't program. Is this an asset to be listed on schedule F of 706?
Once received is this US AG dept to be income on the 1041 as well?
If it goes on the 1041 may I attached a schedule F and pass it through to the beneficiaries on the k1s?