Atmospheric air pressure is about 15 psi, which is essentially indistinguishable from 0 on your gauge. Once you go over say 25 or 30 psi, the gauge will read a bit more accurately. You may get an initial higher (than 15 psi) reading once you connect the pump hose to the tire valve, if some air escapes from the pressurized inner tube.

A well-designed quick-release should ease up very slightly as you close it all the way. The main concern from over-tightening is that it may affect the pre-loading on the bearings. If you notice the wheel is turning less freely, you might have to ease up on the death-grip. If you have external cam quick releases, it is unlikely that you will over-tighten it (but there is more room for other types of user error). It is probably worth getting someone with more experience or a bike shop to show you this in person.