1) Usually 1 per Grav Well, per faction (for instance, you and your ally can put 1 Starbase each in a normal planetary/asteroid/Non-colonisable GW)
however, Stars can host up to 4 per faction. these are fully built starbases btw
2) Only the constructor itself takes up fleet slots. once the SB is built, you get the points back. the SB itself uses no logistics or fleet slots whatsoever
3) i dont have one sorry, im sure there is one around though. but very basically, there are 3 basic ways to use them:
1. is to defend an entire GW in concert with other defenses.
2. is to defend only your planet and structures with it, in concert with other defenses (hopefully)
3. is to use it to control territory in NCGW's and to extend your trade routes, boost culture, or generate extra tax income... (i think, im not sure what the Vasari colony pods actually do...)
one extra note, im sure you realise TEC and Advent have Assault Cruisers (anit-structure cruisers Ogrov and Starfish) while the Vasari dont. that is because the tactic is to jump in a fleet around a SB constructor, built the SB quickly, and use its anti-structure weapons to destroy structures in a GW.
i personally dont line this tactic, its too slow for my liking, but thats just me, and i dont play Vasari anyway
hope that covered the basics for you