How to keep my sink from coming loose?
This is one of those places where a little bit of plumber's putty is indicated.

The problem is that there is little friction between the base of the faucet head fixture and the sink to resist the torque. 

Roll yourself a pencil of plumber's putty about  1/4" dia and long enough to form a ring around the hole. Add a couple extensions straight out from the sides so it looks like the old US Airforce star and bar insignia. If you did it right you will get little or no squeezeout, the base plate will adhere to the sink and you now have a water dam so no moisture can get through the hole. 

Operating the sink handle once you have the faucet assembly tightened down should no longer allow a twisting force against the fastenings.

Don't use silicone caulk to do this if you can help it. The sink outlasts several faucets and having to remove it from the sink is nigh impossible and looks pretty ugly when a new faucet has a footprint that exposes it.