Limits on unanimous consent in parliamentary bodies (namely the Senate)

In the United States Senate, unanimous consent is used in a variety of situations. Any business conducted in the Senate, except for very narrow exceptions, requires a quorum of more than 50% of the senators to be present. However, that quorum call can be waived by a simple unanimous consent request.
As happens at the inauguration of new senators every two years, resolutions are adopted by unanimous consent (communications to the President and to the House that the Senate has convened, or something like that).

What establishes that practice of unanimous consent? Is it a senate rule, or is it a unanimous agreement between senators to suspend the rules?

What are the limits on the unanimous consent? Given that it's used to suspend the rules in the Senate (to suspend the quorum for example), what is the limit on what it can do to the rules? For example can it be used to remove the flibuster if no republican Senator is in the room to object?

Other than things only related to the rules and their application, what texts, motions, resolutions or acts can be passed through unanimous consent? Here are some examples:

• a simple vote requiring 50%+1 votes
• a vote requiring 60% of the votes, per senate rules
• a vote requiring 66% of the votes, per senate rules
• a vote requiring 66% of the votes, per the constitution (for example a veto override, or an impeachment trial's vote to convict, or the adoption of a constitutional amendment)

Among these, what is the limit of unanimous consent? What can be passed by a presiding officer and a lone other senator, happening to be alone in the senate chamber? Are there any recourse agains such actions, a posteriori, by members who were not in the chamber when the unanimous consent took place?