To my knowledge only expiring/closeout type auction buys require a one year renewal with your winning bid price. No other buyer fees that I am aware of. Although, you may want to read through GD ToS for auction buys.
As I understand it, if it's an expired auction it should immediately relist at the next lower level pricing tier. If it's a $5 closeout it should be dropped and become available to reg. If simply another domainer then there is a good chance it will get relisted if it closes without any bids.
Godaddy takes 5 business days to release the domain to your account. Once you make the payment, you can see the date when it'll be placed in your account in the auctions section (under won).