Primary questions

Mitt Romney's win in the Florida Republican primary has put him back in the lead in the race to become the party's nominee in November's presidential election.

I've got a basic understanding of the primary process but there are still a few questions I'm not sure on.

Primaries are run by and paid for by the states, with differing rules as to who can take part. In some states you have to register as a supporter of a party to vote in its primary, in others I think anyone can (except voters registered as supporters of another party: I think that's what closed, open and semi-open primaries means).

Has anyone legally challenged the right of states to run closed primaries? Can smaller parties like the Greens take part in the primaries by reaching so many registered voters? What is the difference between being a registered voter and a member of a political party (if indeed you can be the latter, either at national or state level).

The nominees of the political parties are chosen at a convention. Florida is described as a "winner takes all" primary which I take to mean that all the Florida delegates to the Republican convention are bound to vote for Romney. Do other states allow proportional representation of all the candidates in their delegation to the convention, and if so how?

The Democratic party is also running its primary elections at the moment, which are understandably attracting less media coverage: in Iowa, Obama got 98% of the vote against a handful of fringe candidates. Has any incumbent President ever been unopposed in seeking the nomination of his party? If so, would the primaries still go ahead with one candidate? At what stage in the process is it possible for a candidate to have gained enough delegates for his or her nomination to be a formality at the convention? Do other states still have primaries when the result is already decided? Have there been cases of delegates who vote against the primary result at the convention (similar to faithless electors in the Electoral College which elects the President)? Are "superdelegates" (elected officials who attend the convention ex-officio) free to vote for whoever they want?

Any answers from experts on US politics gratefully received!