The flowing fabric in your sample video was very likely real footage shot in slow motion using the same sheer fabric the singer was wearing and simply keyed and composited over the shot. That's the way I would have done it rather than spend days in post trying to do that kind of fabric simulation in a 3D app. That kind of fabric simulation can not be done directly in AE with standard effects.
You can bend or warp shapes with Freeform in 3D space using displacement maps. Freeform came with CS6 (I believe, maybe CS5.5) so you may not have it available on your system. Freeform will distort a layer in 3D space, but creating a fabric simulation with it using an animated displacement map is going to be a real challenge.
There are other solutions that will warp lines and paths in 3D space. Trapcode (Red Giant software) offers several solutions. Your other examples can be recreated in AE with these and other 3D programs but would be much easier to recreate in a 3D app. Blender is free and open source, C4D Lite comes with CC. Either of these would get you started but are not simple one click solutions.
Here's what a freeform project looks like:
Thank you very much for thorough answer! Unfortunately the machine I'm using AE on is 32bit and cannot therefore use CS6 but CS4. So FreeForm is for now out of question. But Trapcode is available for 32bit, so I'll try this.
If it goes well I'll maybe show the result