RE: REPLACING BATTERY
I don't see it in those pictures. But that is one of the ESC's that I've received from GP that purports to be LiPo compatible.
On the one I have which looks identical to that, there is a jumper on the one side you did not photograph... the side closest to the battery.
The jumper controls the cutoff point to make it compatible with LiPos.
If there is no jumper, you could try running 11v through it, but to be safe run a smaller prop. Step down a size to avoid overheating the ESC.
To play it really safe you could always replace the ESC, but in your shoes I'd just try it, run it up on the ground to full throttle for about 10-15 seconds and check the condition of the ESC.
It should be warm to hot, but not so hot that the covering appears to melt off.
A smaller prop will prevent overdrawing the ESC.