Nope, not at all.
One of the general faction rules is that a offical faction cannot deny access to someone correctly IDed and IFFed to get a ship of that faction, so yah, you don't have to be in the congress to get one.
Yes, no official faction can restrict distribution of ships, capital or not. I also believe they cannot restrict from a guard system even if they did buy it... So theoretically, you could go into liberty and buy a liberty drednaught. (you'd need RP and proper iff too, of course)
Absolutely nothing. You may name the ship whatever you please so long as it does not break server rules for naming conventions. (Chiefly: NaM3z L3|< t|=|is or "LOL-BUTTS")