You may need to set a custom profile in the NVIDIA CONTROL PANEL but you're on a JX, so the dGPU is always on.. not sure what's going on there. Maybe because you're using a different operating system, the internal GPU in the CPU is able to be read from? Not sure.
You cannot game on the G750 while on battery, not properly anyhow.. the CPU throttles down low to between 0.7GHz - 2.4GHz and the dGPU will also throttle too as it cannot get the power it wants to run. Your power brick supplies pretty much 20volts at 10amps, the battery can't support that type of flow for longer than 50-60 mins and it's not healthy for it. Remember, the G750 is a desktop replacement, not a laptop.
Warranty changes depending on country I believe, so you'll have to check it out. I believe the laptop can be opened all the way, but you cannot repaste the CPU. There's a warranty sticker over the screw #1. You will void your warranty if you break something while inside the laptop. (Like accidentally bashing the motherboard with a screwdriver)
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