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I can answer your first question.
After Serie B there is Serie C1 which is devided in two leagues A and B, Serie C1A & Serie C1B. After this there is Serie C2 which is devided in three leagues A, B and C, Serie C2/A, C2/B and C2/C.
I think teams which are in the two levels of the C divisons (C1/* and C2/*) are generally classed as being semi-pro; the Italian Cup which the Serie C teams play for used to be called the Semiprofessional Italian Cup. Or at least thats what Google says.
It was a genuine question btw, mkus. When I start in a new League, like I did recently in Eire, part of the fun is in finding out about the idiosyncracies.
I'm three seasons in and still haven't figured out the Leinster and Munster Cup Competitions, only that I haven't played in either.
Ireland used to be divided into 4 counties (sometimes 5) Ulster, Munster, Leinster and Connaught (Meath was a county at one time). I presume that The Munster and Leinster cups are only for teams in those counties. The counties are still used for Rugby and Gealic sports sides. A map of the old counties can be found at the following webpage http://www.genuki.org.uk/big/Ireland.html
The only real part-time/full-time difference I've noticed is that full-time clubs will happily part with bigger wages. Not to say you can't pay decent wages with a part-time club, it just takes a bit longer for the wage ceiling to build up.