I'll answer in order.
1) Animations that change numeric values (this includes X and Y properties) are relative by default. So they should work with other behaviours affecting the same instance. Relative timelines apply their changes incrementally, so if there are external objects making changes on the same instance, all of the changes will be joint together.
This will result in the timeline ending in unexpected positions.
2) I am not too familiar with animation lingo, but if what you mean by transpose is to use the animation designed in the editor with another instance at runtime, it can be done. You need to use the Set Instance action, which allows you to set the instances that the next timeline you play will use. A more detailed description on it can be found in the manual. C3 has a built in example that uses the action, just search for "timeline" in the Start page.
3) This would also be solved with the Set Instance action. Right before playing a timeline, use the action and when the timeline starts playing it will do so with the specified instance(s) instead of the ones used in the editor. When you use Set Instance C3 is creating a unique timeline for all the specified instances so all of them will have their unique state.
If you need to further control these kind of timelines at runtime, you need to remember to use a Tag when playing, then use that to target the timeline that you need to control.
Hope that is helpful.