The tracker on young witches and wizards was called the Trace. I think Muggles could be transported by Side-Along Apparition and Portkeys and stuff if a wizard was helping them, but I'm not so sure about Floo. Though I don't remember anything being said about this in canon, so you've probably got a bit of freedom with this.
With Molly and the trunks, its likely she could transport them by Floo powder. I think there'd be some kind of spell invovled, but I doubt its a particularly complex one, as its probably quite often used by wizards moving house if one did exist. Again, I think you've got a lot of freedom with it though.
Hope this helped,
Ash
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