I'm guessing a significant[1] proportion would change their mind, when they see the kind of punitive conditions[2] the EU would probably impose on rejoining.
[1] enough to change the result of the second referendum, so >10%.
The reason we had such a deal was because we had restrictions for not being a member of the Schengen or the Euro zone. If we rejoined the EU then joining Schengen and the Euro would be a prerequisite. This is the same for all new members of the EU. There would be no punitive conditions as the EU is based on everyone being equal.
Again no. Because the UK was not part of Schengen or in the Euro zone we could not take on the presidency. Since we will not be joining under those conditions this time then that will not apply. EU rules state all new members must be in Schengen, and must also promise to implement a currency change to the Euro. The is no time frame attached to implementing the Euro.
It's ok, I'm sure Austria and The Netherlands will have UK's back and just veto their Schengen joining ad infinitum for no apparent reason. As for the Euro, the UK can just pull a Sweden or purposefully maintain a highly variable exchange rate so as not to fulfill the requirements for joining the Eurozone.
Alternatively, pull a Denmark and peg it to the Euro and do some voodoo with interest rates when it's in danger of changing parity outside the agreed upon limits. (Not sure if this is what pre-Brexit UK did?)
a) misunderstand the EU's incentives here - if a genuine supermajority in the UK came back asking to be let in, EU leaders have an incentive to make that happen easily as a signal of the total failure of Brexit and hard-line euroscepticism - the optics of the UK returning would be so good for the EU; and
b) overestimate the 'punitive' measures the EU could take - worst we would get is the sort of arrangement other EU states have such as hypothetical future euro membership that neither the UK nor rest of EU would have any more desire to implement than is the case for (e.g.) Poland or Hungary; they wouldn't even need us to join Schengen because that actually would create the Irish hard border that the EU negotiations were all about avoiding (since Ireland isn't a Schengen state).