Some governments have some stuff as contraband in their space and so not allowed, but not once I saw anyone actually stick to it. Beside GE when they needed an excuse to kick someone out. You can have any faction you want, its up to you and the members how you role-play it. My recycling group isn't far from anarchists for example. Although any criminal factions tend to struggle because there isn't much opportunity to do much beside scamming and looting other factions, which doesn't hold much RP value in my opinion.
“Is it possibly to have a mafia with organised crime or
Pirates with ships rum and stolen booty
And so on”
It's possible, but difficult at this stage in the game. Some previous incarnations of Black Sun were a rather effective mafia. Some previous actions of Eidola and a few short-lived pirate groups involved hijacking other factions' ships and assets.
Given enough fortuitous opportunity and cleverness, it's certainly something that can be pulled off from time to time, but for the most part factions begin to develop those reputations and some of that is reinforced through roleplaying scenarios or general attitude of the group members.
So it depends on what you're looking for. If you are specifically interested in means of crime that rely exclusively on implemented features, at the moment you have little choice but to seize opportunities when they arise, because these things depend greatly on the voluntary actions of your would-be targets.