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Welp, first off, I'd suggest to test (or have tested) the battery/alternator to see if its up to speed. This can easily be done with a simple voltmeter.
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Voltmeter won't tell you much about the battery. A lot of auto parts stores can do an actual battery test which will tell you more than voltage, you need to know CCA and reserve capacity too. If you have AAA they'll come out to you and do a battery & alternator test as well.
I don't see how the Evap system and the battery are linked, but a loose gas cap WILL cause that code. Is that the OEM gas cap or an aftermarket one? Is the gas cap damaged? Fill up the tank like normal with 91+ octane, see if that fixes the Evap codes. DON'T OVERFILL EVER- even one overfill can damage the Evap system- have you ever overfilled? P0456 is usually gas cap or a leak in the Evap system. A cheap aftermarket gas cap can cause it too- believe it or not, the gas cap is no longer just a cap for the gas tank, it's a highly engineered car part that can cause problems if you get a cheap one.
The coolant is more worrying. A 2013 car with 27k on the odo should not use any coolant. You need to find out where that coolant is going. Do you see white smoke when you start up (not a small amount like normal, but a plume)? Do you smell burning coolant or have you found any on your driveway or inside the car on the floor? Check your oil and smell the dipstick, is the oil emulsified or smell sweet like coolant? Make sure the radiator cap is on tight.
That said, it's also possible that it got low over time (3 years, you can lose a little coolant) and when you filled it up, what you added to the reservoir got sucked into the cooling system and you didn't lose any from last week. Add more and watch it.