Can anyone tell what is going on in this box?
Actually, no. Not without a fair amount of above-average-amateur sleuthing and a great deal of measuring and testing, which must be done on-site. We can't redpill you on this, at least not in any time-scale one might consider reasonable lol.
As you can see, wires are NOT color-coded in any useful manner. The wires aren't color-coding; they're how cables are made: /2 has black+white and /3 has black+white+red. It's possible to infer some information because of standards over how white wires are supposed to be used, but it's usually not enough.
**The way one electrician documents the configuration to the next electrician is in how the wires are connected already. 3 blacks spliced to 1 white: we know what that is.
It's a trope around here that a novice separates all the wires, splays them out in a big asterisk, snaps a photo and then asks what they all do. Sadly the novice destroyed that information by separating the wires. To recover from this requires a huge skill leap.
Why are there four plain copper wires?
Those are safety ground. 4 safety grounds is strong evidence that you have 4 cables coming into the box. (supported by there being 4 white and 4 black wires).
Grounds are the one simple thing here. Grounds must all be connected to each other, and to the box if it's metal. Metal boxes will carry ground to lamps and switches; all others must also have a safety ground run to them.
Why is there only one red wire?
Because 2-wire cables are manufactured black-white. (plus a safety ground). 3-wire cables are manufactured black-white-red. (plus ground). Conclusion: You have one 3-wire cable in the box.
So far we know you have one 3-wire cable and three 4-wire cables. This adds to the picture.
The fact that there is exactly one 3-wire cable, and the fact that all its non-ground wires were previously nutted together, is a hopeful sign - it means there might be a "modern" switch loop already installed in the walls, if we can find confirmation of that, it'll identify that cable at least.
What is the purpose of the brown bundle of wires that contains a black, white and copper wire? Is this even safe?
I would certainly hope so! That is "NM" type cable. Cable is several individual wires attached together, typically inside a sheath, but not always.
The brown sheath may just be a brand/style, or it has aged, or it's from fire damage.
Also, is it safe to attach this very simple light fixture to it once the fuse is replaced?
Once the various wires are identified and their purpose is determined for certain, it may well be possible to put a light here. You certainly can't blow past that 'identifying' part, if that's your hope. This will require a GREAT deal more skill than you have so far.
It's certainly possible to attain that skill, but this won't happen overnight. Given the complex task of analyzing this 4-cable network, the only fast way is to hire a pro.