This is know as a third-party check and most banks accept them if properly endorsed. You need to sign the back of the check, then write "Pay to the order of" + the name of the other person. The person who owns the account will have to sign the back of the check as well. Don't expect the check to be immediately available, the bank will most likely hold the funds for a few days until the check can be verified.
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Yes. You will have to endorse the back of the check and the person who's account your are depositing it into will also have to endorse it. There will likely be a hold put on it so the funds can not be withdrawn until the check is verified.