Whose National Treasure?

I have just finished watching a DVD of National Treasure starring Mr Nicholas Cage. This is a well executed but vacuous Indiana Jones pastiche with elements of the Da Vinci Code. See USCCB review here. The revolt of the North American colonies is depicted as a Masonic plot (seems fair) and the Masons are depicted as mankind's secret benefactors (oh well). Strangely however, the missing link in the Masonic plot is supposed to be Charles Carroll (1737-1832) the last surviving signatory of the rebel charter. Carroll was a Catholic, and - the way I heard it - the only signatory who wasn't a Mason. So, questions for more informed readers...

1. Was Caroll a Mason?
2. Were all the other signatories Masons (as is often said)?
3. Why did Caroll sign it if he was a Catholic and not a Mason?*
4. Is it true that every US President apart from Lincoln has been a Mason?

* One may only rebel against a legitimate government (and George III was recognised by the Holy See) if it is grossly violating Natural or Divine Law and one has a moral certainty that the rebellion will reverse this and not produce greater evils (CCC 2243). 'No taxation without representation' is obviously an article of neither Divine nor Natural Law nor does the right of ex-pat. colonists to send members to the House of Commons appear in any statute I know of. To this day not every citizen of the UK has the right to vote in general elections (Lords, Convicts, under 18s etc.) and more-or-less universal franchise was unheard of on both sides of the Atlantic until the twentieth century.Indeed, it could be argued that insofar as anyone was trying to remedy violations of the Natural Law it was George III.