1. Yes, there are many descriptive terms for tree crown forms "vase shaped", "cone shaped" etc. At the most basic level the crown form can be described as "excurrent" which is typical of conifers or "decurrent" which is more typical of broad leafed trees, like oak or maple for example.
2. Not that I know of. In rec tree climbing we talk about limb/branch routes vs. trunk routes. I think of it as either an air route (no contact with the trunk for the initial ascent) or a trunk route.
3. In rope and harness tree climbing the goal is to constantly remove slack from the rope as the climber progresses. That is known as "work positioning" climbing meaning the climber wants to have their weight on the rope as much as is practical. Tree climbing ropes are very static vs. say rock climbing ropes. It is is extremely dangerous to climb for long with slack in the rope (weight off the rope) in tree climbing. "Fall factor" forces multiply exponentially with increased slack and static or semi-static will transmit that force to the climber's body if they fall on a slack rope.
4. No, the way you describe it is accurate, there is no specific term for that as far as I know.
5. Not specifically. Rec tree climbers typically climb what's called "doubled rope technique" or DRT so the TIP need to be isolated. In single rope technique or SRT, climber security is improved by distributing the rope over multiple support points in the tree.
6. See number 5, in SRT line settings, I call it a "distributed TIP", others may use different terms.
7. No, there isn't a specific term that I know of. Tree work climbers typically maintain a strict protocol of always having a route to reach the ground without having to down pitch or re-pitch on the way down. Mileage varies with rec tree climbers, I frequently re-pitch above where my rope can reach the ground in one or more down pitch. For example when climbing in tall forest trees where I have to carry gear a fair distance and it is not practical to carry large amounts of rope.
-AJ
