If it is an auction, which starts at $10 and you bid $10, and no-one bids higher than you, then yes you will get it.
Domains at other registrars can be listed at tdnam, but I have never come across any - i have bought and/or sold around 100 domains on tdnam.
it's always best to check the
whois to see where it is registered.
If the domain is an expired auction, then yes, godaddy will put the domain straight into your account after the redemption grace period has finished.
(assuming the old owner does not renew)
You will have to pay a 1 year renewal.
If the domain is being sold by the current owner, then you will contact them after the auction ( or they will contact you ) in order to arrange the account change / or push / or transfer.
In this case you will not have to pay extra fees, unless you decide to transfer the domain from one registrar to another. The usual process is just to push the domain to your account at the same registrar.