Wow, you guys hae done a lot with Creo! Below are some general, theoretical answers to your questions. These are tough questions to answer without having the models and understanding your design.
1) There is not a "String" connection. You could maybe simulate this by applying a force in the direction that the string would be pulling. Another option would be to create a Sketch or curve feature representing the string. You could then create a datum point on the sketch (using the ratio option). If you assembled to that point (on the string), then when the point moves, components attached to the point would also move. This would not be a Mechanism type connection but you could move the components by editing the point, then regenerating the assembly.
2) You could model a zip tie in a number of ways, depending on your needs. Extrude the shape or create a curve (sketch or through points), then sweep the profile of the zip tie along the trajectory curve. Depending on how the part is created, you could then make it a Flexible Component to show it in different assembly states. If you used the curve through points method and the points were on different components of the assembly, the curve (trajectory of the sweep) would change as the position of the components changed.
3) I think the CAM type connection in mechanism mode would help with this.
I hope this helps!