Yes, but there will be a comment on the account stating something along the lines of 'legally paid less the full balance'.
Yes it will be $0 balance. Settling a debt means you have negotiated with the lender and they have agreed to accept less than the full amount owed as final payment on the account. The account will be reported to the credit bureaus as "settled" or "account paid in full for less than the full balance"
Yes, but make sure to get it in writing first. Some lenders (and especially debt collectors) will not honor their verbal agreement after receiving your payment and continue to try to collect.
