I recently had an expansion tank installed by a local plumber, he also installed a new PRV valve. The plumber set the expansion tank at 65 psi he said he set PRV at 65 psi also but didn't check the pressure with a valve he forgot to bring one. I am getting noises around tank when I turn hot water on. I went out and bought a guage and see my house pressure is about 53 psi. Does the expansion tank still function properly being set at 65 psi, and could this be causing the noise when hot water is turned on?

as the saying goes "we wouldn't be plumbers if we didn't forget to bring something".
the expansion tank will work just fine. at the current pressures. all it does is absorb excess pressure.
since you have a gauge, if you want to get a little more pressure for your self, adjust the PRV upwards a few pounds.

quote: I am getting noises around tank when I turn hot water on

yes that's something to look into more if it's coming from the expansion tank.
Maybe a simple correction of pressures will stop this noise.

If the bladder in the tank does fail the tank is worthless and thermal expansion can cause more problems.