4
The 2 black + 1 white is your always-hot bundle. You won't use it (unless you want to power the fan 24x7 and use a remote on it).
The 2 white is the neutral bundle. Your fan will need that.
The loose black is the switched-hot from the switch. (it is the partner wire to the oddball white from above). This is the switched-hot for the fan.
The switch ...
3
...ever seen lights that use this kind of box for hanging?
No, because that box is not made for directly attaching anything to it. The box needs an adapter ring attached to hang a standard fixture (or to mount switches, receptacles, etc.)
By itself that is just a junction box called a "4-S" (for 4" square). Look for a 4-S to 4-O plaster ring.
It goes ...
3
Without being able to see the clips, I’m still going to say to try placing the lip of the glass cover against two of the clips and then press against the opposite side of the cover: use the cover to press in the clips. You can then use your other hand to press in the remaining clip.
You may actually find that one of the clips is fixed. In this case, use the ...
3
Yes, but you won’t like it...
Had this before, and you have to remove the old paint back to a secure, stable layer.
Think yourself lucky - we had to do it on the ceiling of a paper mill.. hundreds of square metres...
2
I would scrape off the paint in that circle to see what is there - you might find screws etc
If not then I have used a bradawl in the past to find the joist - usually light fittings are close to joists for support or an extra piece of wood is fitted between two joists to provide support.
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