In form 1099-DIV, under Additional Payer and Recipient Information, Do I use my address for recipient ?

Yes, you are the recipient therefore you will use your address.

To enter Form 1099-DIV:

1. Click on "Search" on the top right and type “1099-DIV”  
2. Click on “Jump to 1099-DIV”

I have a question about the recipient.  If this is a nominee distribution from a decedent's final tax return and the distribution goes to the Estate, what address do you use for the estate?  

The mailing address reported on the IRS Form 1041 tax return.