Clock changing time & Fuel Gauge not accurate

Over the past few months I've gotten in my 2011 Chevy Aveo and the clock was a completely different time. It hasn't happened in a little over a month.

Friday after work I filled the tank and drove 20 miles home. It has not been driven since. I got in the car this morning and it was on E. I checked where I had parked, no leak. I drove towards work and after about 10 minutes it said I had 1/4 of a tank. By the time I got to work it said I have 1/2 tank. It should easily still read full.

Could the two issues be related?

anyone have experience with this?