shipping disruption happens when a merchant fleet heading to one of your colonies doesnt make it. your system probably doesnt have the capacity to produce every commodity your colonies need so it'll basically always be a possibility for a fleet from the core to not make it -- through no fault of your own. it's just a thing to live with
as for why your colonies arent trading with eachother, that comes down to access. the accessibility stat determines how much of a commodity can come from your other colonies (on top of other stuff). raise that stat & they'll supply eachother more. there are, however, very few ways to actually do that. build waystations, upgrade ur port, upgrade your waystations & megaports