So a couple things on the go here ... First to address the how water ... The water tank is on a concrete floor now? Because concrete will conduct cold and contribute to cooling the water inside the tank. While they are insulated, the tank will still have some thermal conductivity. You may want to consider raising it off the floor a bit.
Second, for the wobbliness ... a few things ... Where is your drain for the tank? How level is the floor? Is there something under the tank? Worst case scenario, have someone build a "stand" for the hot water tank and raise it up off the floor a bit. I did that with mine but also added a "catch pan" like this one from amazon just incase the tank ever leaks.