What is Tina's wish card used for and how do I use it ?

You mean tiny's wish card? It is obtained thru finishing the ferris wheel event and can be used in the school of architecture, after using it u can obtain the ferris wheel in the "landscape" section on the build tab, it costs 3 thousand gems to build it, it might sound expensive, but it looks nice and can be a good souvenir from the event alongside the South pole research station :P, hope this helps.