There should never be a problem operating a transformer on lower
voltage than it was designed for. The problem comes from operating on
too high a voltage (and usually that problem is core saturation at line
frequencies--or core overheating for high frequency transformers).

As for charging the batteries, you can find lots of info on "doing it
right" on the web. I've found
http://www.batteryuniversity.com/partone-13.htm to be pretty good. It
saves a lot of work if you have a circuit do the monitoring for you,
but you can do it yourself with voltage and current meters. If you get
tired of looking at the meters, check out TI's UC3906 and related ap
note.

Cheers,
Tom