This isn't a huge deal/issue for me and they work fine but I just wanted to find out why they aren't reading properly.

Recently put in a new thermostat, and after the first 5 minutes of driving the car the needle goes all the way to hot, then back down to what it was normally reading and it stays like that (it only does it once). Never used to do this, should I be worried?

The fuel reading has me a bit worried too, sometimes the needle will go up or down, by quite a bit of a margin, for a few minutes. Then it will go back to what it was, and happens while I'm driving. Also when I fill the tank completely, the needle will not move from the full line for at least 60k's, then it will start to go down. Been doing this for a long while now, wanted to sort this out.