canastasiou6

The Intel AX200 WiFi adapter will provide you with Bluetooth 5 and WiFi 6.
 
Any Bluetooth adapter should be easily able to maintain at least 2 simultaneous connections. That being said, BT works best at short distances (so make sure that the antennae are within line-of-sight of your client devices) and with little/no wireless interference.
 
So don’t expect antennae/adapters mounted at the rear of your computer to function as well as those mounted at the front. I learned this with my SFF PC; used USB extensions (male-to-female) to get the USB dongles facing the controllers.
 
Furthermore, any 2.4GHz wireless activity can slow down Bluetooth. If you’re not using anything on 2.4GHz WiFi, just turn off the antennae at the wireless router... or at least limit its power output.

Ethernet network cards have isolation transformers on them, isolating all signal pairs from the network card.
On onboard network cards, the isolation transformer is often hidden inside the actual connector.
 
Transformer on network card:
 

 
Transformer hidden inside the RJ45 connector  : https://www.digikey.com/product-detail/en/abracon-llc/ARJ-196/535-13148-ND/5430433
 
 
 

 
Explanation on stack exchange for the reason (simply because among first search results) hardware - What is the purpose of an Ethernet magnetic transformer, and how are they used? - Network Engineering Stack Exchange
 
 
If you shove AC on the ethernet cable, yeah, if you're unluckly you may damage the transformer on the ethernet card (transformer's wires are super thin so they'll probably melt) and maybe even get the network card to die but your computer won't be live and there's no risk of you getting shocked by electricity.

The wire itself has insulation on it, the pvc/pet/whatever colored material ... if there was no insulation the wires would touch each other.  The insulation is dielectric, it doesn't conduct electricity.
Two wires at a time are twisted together and they're separated by the other pairs by that middle + or x  channel usually made of plastic ... well, a proper cat6a cable would have such a plastic core to separate the twisted pairs, yours may not have it if it's only cat6.
Then, the sleeve of the ethernet cable is a second level of insulation ... it's not shielding because shielding would be an aluminum or copper foil wrapped around the pairs of wires under the sleeve, or a mesh of aluminum/steel/copper wires wrapping the pairs of wires.
Either way... like i said, there's two layers of insulation protecting the internal copper wires (or aluminum if CCA cable) from mains.
 
 

You could just get shielded ethernet cable but even with regular ethernet cable you'll probably be fine routing the cable along the AC cables. The AC noise would be low frequency and the wires inside are twisted to reduce interference, and you have multiple layers of insulation on the ethernet cable. By design, there's signal transformers  on network card and switches/routers/whatever so even if live AC would get into the ethernet cable, your devices won't die or kill your pc.
 

If you have Asus board I THINK you can use Gamefirst to do what you want. It maybe have to be ROG board, I don't know but look for it where you download the drivers for your mobo/laptop.

This is most likely a ground loop issue and interference with poorly integrated electrical grids in your home/area. 
 
I will note that adding an external sound card will not help this, and often will make it worse- that ground loop interference is now no longer being shielded by the motherboard's own shielding, and they generally have none of their own. You can get isolators and shielding for this but I never had to and don't know what to go for.
 
I do wanna note that several Xonar cards (as mentioned above) in my humble opinion greatly improve sound quality over onboard- especially on budget motherboards, budget motherboards (under $300? probably bad onboard) slack on the clarity. Those xonars are the most affordable onboard if you really don't want an external DAC/AMP. The DGX is probably the best for your purposes, but is out of your price range. The DGX has a good amp system, and a few features that make things like streaming much easier.

Do others hear it? If not then there is no problem.

For 60€ you are not getting anything that's better than the built in soundcard. Also what interference is happening?

I have a ASUS Xonar DSX. In combination with a good headset it is great.