For PiP, there ARE several Presets to accomplish that, but one can also create PiP manually, by adjusting the Fixed Effect>Motion>Scale and also Motion>Position. If one does this manually, they have much more control, and can Keyframe those Effects over time, so that they change.
As I seldom find any PiP Presets, that do exactly what I want, I always go the manual Keyframing route, so am not the "expert" on using those Presets, but others can help you those.
Regarding your specific question...
(1) How can I remove\delete an PIP FX effect off a track, once applied, that I decide I don't like. I see no option for this anywhere.
How you applied the PiP effect will direct the answer, but just one possible scenario
a. You have applied the PiP to a video clip on Video Track 1 by dragging one of the PiP effects into it. There is no "PiP" Panel in Applied Effects/Applied Effects Palette as there is for several of the applied fx Effects. These PiP work off the Motion Panel properties. Provided you do not have any keyframing done before the PiP application, then go to Applied Effects/Applied Effects Palette/Motion Panel expanded and remove the keyframes that might have been placed there by the PiP effect and take the Scale back to 100%.
Regarding your specific question
(2) On a track, if i want to apply two different PIP effects ( say... one a start of track, and then switch to another mid-way through the track) how do I do this, other than cutting the track into multiple parts?
Cutting the video clip into multiple parts is probably you better alternative. But....you could look at duplicating the clip, placing it on Video 2 directly above the original on Video 1, and applying one type of PiP to one and another type of PiP to the second and then keyframing the Opacity of each accordingly. As I suggested, cutting is the better of your alternatives.
Those are my initial thoughts on the questioned that you posted. Please review and then let us know if any worked for you.