I think you should post some pictures of what you have because something doesn't sound right. If it's a Tamiya Blackfoot the truck is powered by a 7.2v NiCd or alternatively NiMh (same voltage, higher energy density) battery pack that's made up of 6 C cell size batteries. The transmitter on the other hand probably uses 8 AA size batteries. 7.2v NiCd packs are going to be hard to find and you don't want them when NiMh is readily available and much better performing.
To answer your questions
1. No idea, really gotta see pics here to be sure.
2. Again need to see pics, but no it probably doesn't stop charging automatically.
3. Lipos are safe, when used properly. Lipos need a charger that's specifically for Lipos or has a lipo charge mode, otherwise they become unsafe. Lipos also need an esc with voltage cutoff or a separate voltage alarm to alert you to stop running as running the voltage of the pack too low can hurt them.