Usually the first connector is rated for higher current because the wires are thicker and the connector is a HCS type. So it's better to use the first connector on the cable than the daisy chained connector.
Don't know what happened inside the case but it's a mess. Some motherboard screws are missing, the GPU is not mounted to the back of the case and the PSU is old junk. When did you buy this >10 year old system?
You don't want to power a 1080 Ti with a junk group regulated PSU like that. It's a bad unit because the voltage regulation is horrible and it lacks essential protection features.
No, only upgrading to a more silent PSU would stop the noise. Take a look at the noiise chart in https://hwbusters.com/best_picks/best-atxv3-pcie5-ready-psus-picks-hardware-busters/4/
There's no reason the get 750w if 850w costs the same.
Decent 850w ATX3.x units for a reasonable price:
https://au.pcpartpicker.com/product/dtHqqs/cougar-gex-x2-850-w-80-gold-certified-fully-modular-atx-power-supply-gex-x2-850...