Chosen Solution

The small part of the Microphone arm under the left ear side of the headset shell is torn in half leaving the rest of the arm hanging (no wires damaged from this thankfully). I was wondering if I should use hot glue or some sort of electric glue if possible? Tape would just hold it on for a certain amount of time. I got this headset in January. I would love to fix this asap and try not to damage it any further!

I would put some glue onto one side of a small piece of tinfoil. Then wrap the tinfoil around the broken part of the mic boom to hold it in place temporarily. Once this is done, carefully place the headset in the oven for around 30 minutes at 160c. This will soften the plastic nicely and allow the boom to melt back together.