This is best done in Blender (if going the free route). It has a great solver. Then render the top layers (no video background) with transparency and pull it into Shotcut. This separation of duties is somewhat ideal because the feature set of a formal compositor (Blender) does not clutter the simplicity of a video editor (Shotcut).
Same thing. Design in Blender with the full capability of a 3D modeler, then export and bring it into Shotcut.
Transitions are user-definable. You can create or find as many as you want. Your other thread lists many resources:
Shotcut already has this. Look at the “Stabilize” filter.