Well, it wouldn't be the first engine to pull more than 1,500hp. The Renaults were pulling that amount of power from their F1 cars THIRTY years ago. And the engine was half the size. Sure they only ran that hot for quali, but with double the capacity and 30 years of technology, just matching the power shouldn't present much of a problem.
Packaging it and the cooling should be fine also - it doesn't need gigantic intakes because at an average speed of 200km over a lap the volume of air passing through it is colossal. The gearbox and diff would have to be especially beefy though; superfast shifts with that much power at that speeds does put a lot of load on it.
The fan, well that's fairly straightforward. Just hook it up to the engine by whatever means, done. Getting it to vent cleanly from under the engine and managing the tubing around the engine/gearbox/etc could be interesting, but not impossible.
The tyres...well. The Veyron's tyres are rated for a 2 tonne vehicle at 400km/h continuous top speed for 10 minutes, and lateral G of about 1.5
So, using extremely simplified math (deal with it, it's late), that's 3000kg going sideways against the tyre. The X1 weighs about 500kg and pulls 8g, so that's ~4000kg going sideways at peak load. (incidentally, a F1 @ 600kg and 5g = 3000kg going sideways). So the tyre has to be 33% better than those grooved slicks they used in F1, and stand up to it.
Not been done before, but seemingly not impossible. You won't get long out of them, but they shouldn't explode instantly, in theory anyway.
From an aero standpoint, it all looks about right based on current trends (LMP1/2, mostly) and what's ideal. Medium fins, wider, lower wings (or narrow wings sitting between the wheels), getting airflow inside the rear tyres, etc.
The only possible problem right now is structure - the pylons holding up the front wheel covers are the wings (attached to the wing, attached to the mount, attached to the nose = too many joins that could cause bending and therefore scraping) and the nosecone mounts (one piece, could bend under aero forces at 500km/h?). Beef those up and it should be right. Also the rear wing mounts might use a bit of a beef up.
The diffuser is also an interesting piece - the 'floor' starts underneath the rear bodywork, then curls up to become the outer diffuser, just inside the rear wheels. There's some pretty severe forces that act in that area, maybe it would need to be thicker?
The rear wheel covers would need some sort of bracing as well, so they don't buffet into the wheel and cause the rears to stutter and grab.
Also, in the interests of safety, they MAY want to do something about it's performance in a sand trap. The smart money's on it's launching a bit, then becoming a lawn dart, launching some hapless driver out the canopy and into the crowd.
