The minutes are a record of what was done at a meeting. Approving the minutes has to do with the accuracy of the record and not with the validity of the actions taken.
RONR does not require someone to be a member to be nominated or elected. It appears your rules might, so the answer to your question would have to be found in your rules.
Generally yes to your questions. A bylaws amendment could be amended using the motion to amend. How much that could be amended is limited to the scope of notice of the amendment.