How do I connect this 3.3V system and 6V ish system together?
It looks like it should work fine at 3.3V. Each connection will draw about 3 mA of current from its RPi output. Yes, you need to connect the grounds together as well.

Gotta love the low-battery indicator circuit &mdash; it just wastes power until the battery is low enough to allow the LED to light up!