You probably haven't hurt the RX by plugging the battery in there.

As for the gyro, one of the wires will be black. That's the ground or - wire. On the gain lead, that has only one wire, that's the signal, which goes at the opposite end to the ground.

In general, most of this stuff is pretty robust against being plugged in the wrong way... but don't tempt fate, double check before you do things. Black or brown wires are always negative, so you can tell by that.