Will I lose my rank if I uninstall and then install the game?

No, Z has all the user data on the servers and it can't theoretically be lost. I don't know if you have android or apple but on apple you just reinstall the program and log-in again with username and password. When I redid it on mine I had to "purchase" the program again, but apple knows that I already had paid for it so they didn't charge me again. I just had to click the purchase button and act like I was purchasing it.

Yeah, you might temporarily lose your subscription -- but the purchase should be renewed once you reinstall.