Since the US Constitutional Quorum for most purposes is a majority of each house of Congress, can bills pass that house with a majority of the quorum or do they need a majority of the total seats of that house to pass?
Can a Presidential Veto be overridden with two thirds of the quorum, or is two-thirds of the total seats required?
What are the like requirements to propose a Constitutional Amendment?
What also are the requirements to change the procedural rules of the said House only?
Do Joint Resolutions have the same requirements?
Theoretically a bill could pass both houses with only a single Senator and a single Representative present. The Senate and the House both have rules that assume a quorum is present until someone challenges that fact, in which case a count is actually taken to determine if there is a quorum present. The constitution defines a quorum as a simple majority, so the Senate requires 51 members present and the House of Representatives requires 218 members. The required number of members for a quorum is also adjusted should there be a vacant seat at that time.
The U.S. vs. Ballin established that a majority of the quorum is sufficient to pass a law. My reading of this senate pdf outlining veto override procedures indicates that a two thirds majority of the voting members is required, which could be two thirds of whatever quorum is present.
The rules appear to be the same for amendments in the Senate, in that two thirds of the quorum is valid. I couldn't find anything relating to the House but I would assume similar logic would be used.
Joint resolutions are work the same as other bills and are the vehicle for proposing amendments so they would also be passed by two thirds of present members, assuming a quorum.
Modifying the rules is a bit different, Both houses have rules in place that require a super-majority to change the rules, again a quorum being present. The nuclear option exists in the Senate, which allows the majority leader to effectively alter the rules with a majority vote even though the rules state a three fifths vote is required. This was done recently to prevent filibusters of appointments in the Senate, but otherwise had never actually been used due to other political concerns.