You have your hands full...
I myself have 4 yorkies
I believe that you are right about older ones being territorial.
I think you should let them get use to each other as much as possible(also mix their toys and blankies)
About diarrhea, I had same problem with my youngest when I first got him. If diarrhea continues over couple of days you should take him to the vet, and he'll most likely give you something called flagyl liquid(smells like fish)to stop it. My breed used "eukanuba" and I changed to "Wellness super 5"(many people in YT use it) and my baby(1.5lb @ 6month) is very happy.