You can travel faction any gates. The only difference is your faction gates are protected with your patrol (native enemy faction patrol will attack on sight), other factions grid have 7 seconds timers to leave the zone.
Usually - it's hard to say. I'd say family. But then again, you may see 7 family online and 3 v-tec, then family get offline, v-tec comes online and they are 10.
There lately many late (american time) players in v-tec. Family is more active at Europe evenings. Lawyers mostly have a little less number somewhere between, and same on weekends.