The answer to all three is it depends. unfortunately there are no standards. It really depends on what you can negotiate.
What you definitely should do is get everything in writing. In minimum confirmed in an email, but ideally a document that spells out the details of the agreement (who owns the design, what the payments are and when they occur, if based on royalties how units are accounted and when i.e. counted when made or when sold?) and bonus if you get a signature on it. It is always better if these things are clearly written out in plain language to prevent disagreements later. You don’t want to loose a client and a friend at the same time.