If I were to mount a pair of speakers behind me, that would require approximately 15 feet (4.5 meters) of speaker wire from my PC to the speakers. Do I have to worry about the AUX port’s power output if I were to use 18 or 16 gauge speaker wire?
I'm pretty confident but not 100% sure, I'm on my phone and only skimmed the manual.
Impedance isn't the issue here, headphones are completely different - their tiny speakers need significantly less power to drive them. I don't think the motherboard is capable of moving the cones in the speakers OP linked
The giveaway here is the inputs - your headphones have an aux (or 1/4"?) input and these speakers have speaker wire inputs
Unfortunately not, the motherboard only has a preamp. Those ports output a line level signal and the speakers are expecting speaker level which is post-amplification which is a MUCH stronger so it will be extremely quiet - if not completely silent
You can buy a cheap 2ch amp but I think you'd be better off with different speakers. It wouldn't be a bad idea to get a second set of whatever you're using for the front speakers to match the sound profile