DIY

Check if you can find some pavers that are the right size. It could make the job a lot easier for very little money. Just drill matching holes into the paver(s) and bolt in place.

Should I put some bolts in the concrete before it cures or should I drill the concrete after it's cured and put some bolts in then?

There is some existing concrete in the spot from the post of our previous mailbox, is it ok to just cover that over with the new concrete?

I'm not a structural engineer of any kind, though I do think that if you pour new cement atop the existing concrete, then it might make the most sense to drill holes afterwards, and sink threaded rods into the holes and secure with anchoring epoxy. Since the new concrete needs to be fairly flat and level for this mailbox to sit atop, you wouldn't want to make the surfacing effort any more difficult than necessary: having four bolts sticking out of wet cement is going to get in the way when you're trying to skim.

Also, if you can drill down into the existing concrete, that may afford additional anchoring, compared to bolts that don't penetrate that deeper layer. The drawback with drilling is that you must not drill down to soil, since I think anchoring epoxy is meant for pull-out strength, not to bear downward loads. But since the mailbox sits predominantly on the slab and the bolts ostensibly just hold it down, this may not be too big of an issue. Just try to control the hole depth it using anchoring to epoxy. Expanding bolts are also an option, but not in all jurisdictions and sometimes fail due to corrosion.

Will it be enough to just make a box shape with some scrap wood for the form or should I get something else? Being a 40 kg monster, how thick should I make the slab?

I'm also no expert on forms, but seeing as the form is discarded afterwards, I don't see why scrap wood wouldn't work. It does, however, need to be sturdy/thick enough to contain the wet cement without bowing, and ideally be removable without leaving chunks of wood attached to the slab. Also, the side which touches the cement should not be too dry, since it'll absorb water from the cement; painted scrap wood would probably be fine. Here in the USA, for small projects, we tend to use 2x4-inch boards (approx 37x88 mm) for forms, and might be aiming for a slab thickness of approximately 4 inches (100 mm).

As for the weight, 40 kg does not seem too onerous, assuming the mailbox has a flat bottom and its weight is evenly distributed. The average American man weighs 199.8 pounds (90 kg), and probably has two feet about the same footprint as that mailbox, and a 4-inch slab would easily support more load than that.

Another commenter suggested using pavers, but it's not clear if they meant pavers for a patio (ie thin, mostly decorative) or pre-cast concrete slabs (eg for an air-conditioner consenser). Patio pavers could support the downward weight, but wouldn't support the mailbox for sideways loading, such as the wind or someone leaning on it. Pre-cast concrete slabs of sufficient thickness (maybe > 75 mm ?) would work, but might be way too large and you'd have to cut it down to size.

If you were installing over soil, an option might be to use concrete cinder blocks, packed into the soil. But this depends on whether the mailbox can sit atop a single block. And you'd still have to drill the block to add the bolts or threaded rods.