You don't need to be any more aware about low batteries with the 6i than with any other radio. NiMH batteries can be safely charged within the airplane using the wall charger (C/10).

First of all, you need to make sure your tester puts a load on the battery. You'll have to read the instructions to find out. Mine doesn't, so I used some resistors to create a load. A 4.8 volt flight pack should read somewhere around 5.35 when fully charged. When the pack dips to 4.7 it is pretty much dead. Remember, however, that voltage is not a measure of capacity (amperes are a measure of capacity), but because voltage and capacity are linked through Ohm's law you can find a fairly predictable 'dead voltage' for the NiMH battery chemistry.

NiMH batteries don't need much maintenance. You really can't overcharge them with the wall charger because the charging rate is so slow (~C/10). I usually cycle my batteries at the beginning of the season to make sure they are at least 80% of rated capacity. If they fail to cycle at 80% they are relegated to a non-critical application. I usually cycle once mid-season or so as well. There really isn't much you need to do to keep them going.

It's a good idea to top off batteries before you fly again UNLESS you really know your particular battery. I keep an extensive log for all my batteries, however, that's probably overkill for most people. I'm one of those nerds that gets turned on by seeing charts and numbers.
Batteries just sitting there will slowly discharge themselves because of internal resistance. Therefore, if you charge your battery and wait a month to fly your battery will have noticably drained even though you didn't use it.