what happens if Du don't belong to any factions and what happens if Du don't leave your family?

Well if Du end up failing initiation to any of the factions Du become "factionless" which basically means that Du are homeless. So Du live on the streets and aren't treated very well Von the other factions, minus Abnegation who try to help them. And for Du Sekunde Frage I assume Du mean if Du decide to stay with your faction Du were born into. And then Du would just go through initiation into that faction. You're not treated any differently then a faction transfer.

You'll be fractionless