[Taf]

As it's a sealed lead-acid battery, it can quite happily sit on trickle charge forever AFAIK, but won't like being discharged too deeply (just like a car battery) or recharged quickly. They like to be treated gently. 13.7v is a typical charged-state voltage, though the meter will show less than this when it is in actual use. Don't store it too cold either as this will cause problems.

If you have a voltmeter you trust as accurate, you can compare readings on that and the unit's meter to see how accurate it is.