Advice on fuel economy for my new used 2010

I think you should suspect that what you are seeing is "normal" for that car and your driving habits.
And gas mileage often suffers a bit as winter approaches.
Tire pressure can go down a bit.

I know it is a different model but my C will run the engine any time that it NEEDS any more than just a tiny bit of energy to maintain speed and certainly to accelerate any at all. This means that the engine NOT running is the exception and not the rule.
IF you can find a long flat stretch of highway with light traffic, you can test this yourself.
There should be an "energy monitor" screen available to show you where the energy is coming from and going to.

Sometimes the engine runs just to charge the battery or to keep it up to operating temperature.

While some of the things you observed can be an early sign of a failing hybrid battery, I think it is WAY too soon to be chasing after that.
Getting your 12 V battery tested would be a good idea though.

 

the battery sitting one bar down is very strange around town. on the highway, it can happen. i would definitely get a hybrid battery module readout.
with the heat off, and engine warmed up, you should be able to drive slowly and watch the battery charge go down, unless your in frostbite falls

 

Have you done any out-of-town trips, resetting a Trip gauge at the start, to get an MPG for a single 10+ mile highway run?

The cold rainy weather of the past couple months here doesn't help. Tire model (e.g. models that are not low rolling resistance) and excessive disk brake drag can also contribute.

Skim this questionnaire for more ideas, though note that it was written for people driving new cars, not older cars that may have accumulated some problems with age:

Fuel economy complaints/queries? Please copy, paste & answer these questions, esp. if you're new | PriusChat

If the hybrid battery is staying high more than expected on slow city streets where it is expected fall, I'd more suspect something elsewhere keeping the ICE on too much, not the battery itself.