What fixings go with the back of this mirror? Are they meant to be used with a special type of hook?
The mirror weighs about 4kg.
I sort-of went with the cup hooks solution but found these hooks and used then instead.
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That's very unusual for those of us in the USA. Your outlets say you're not in this country, though, so it may be more common in your locale.
My guess would be that there is a special bracket made for that - I'd suggest that you check back with the retailer that sold you the mirror. If you bought it 2nd hand, head to the local hardware store or big-box DIY store to see if they have something similar.
Barring that, a pair of cup hooks to go into the slots at the end would likely hold it. At only 4Kg, a pair (maybe big cup hooks) should be sufficient if you ensure they hit wall studs.