Here to answer your Qs.

I have a full set of human hair clip in extensions, 9 pieces, Is this holder for clip in extensions too?

Yes, it holds clip in extensions perfectly!

Is there a trick for getting the holder to suction on a tile shower?

The trick, is that the surface you are trying to stick a suction cup to must be COMPLETELY SMOOTH and NON POROUS. Natural stone, like travertine or marble is porous and will not hold suction cups. Also, if you put the suction cups over a grout line, it will not hold either. A suction cup must SEAL to the surface it's attached to, meaning no air can get under the suction cup. 

Would this work for halo extensions with the invisible wire?

It really depends on the kind of the halo extension you have. The inside dimensions of the caddy are about 1" x 5/8" x 9 5/8". We tried it with the Halo Couture extension and the Halo Couture did not fit ... the lace backing is too wide to fit in the caddy. Hope this helps!

will it hold tape in hair pieces?

Yes, it holds tape in's perfectly.