I've been thinking of our tree as One Tree.
When being lax, I've been thinking someone is connected to the One Tree if they don't show up as "unconnected" per the utility on the Find menu. In my heart though, I'm afraid I see more profiles as technically unconnected than that search does. For instance, for me, though I know the names for a few generations back of my direct paternal line, that line dead ends until I have some major genealogical breakthroughs. So, all those Franz Keils do not show as unconnected per WT's utility, but as far as I'm currently concerned, they are as I don't know of any of their siblings, etc. and don't know anyone living today to whom I'm related through them as a common ancestor.
Regarding question 3, how to describe the connection when someone is a direct descendant of someone in the One Tree ... I'm not sure I understand what you may be getting at ... Like, why would I describe the person's connection to One Tree any different than I would in any other context?