Wheel centers - yep, you can usually find something to fill the hole. Whether or not it has a Lotus logo on is another thing though, but you can buy plain center caps in several sizes to suit most wheels you could buy I guess. You might need a bit of modification to get them to stay in place on an older wheel design, but nothing too drastic. On my 1970s Cosmic wheels I just made up some blanks from sheet aluminium, stuck on a resin Lotus badge and held them in place using the original Cosmic wire spring arrangement. (like in the attached picture).
The 15" wheels that I will eventually get around to fitting came with domed MG centre caps because they were for an MGF. So far I've removed the MG logo, used body filler to get a smooth finish and they'll get the same resin badge treatment after I've resprayed the wheels & caps to match.
Cooling. Well over on this side of the pond we don't have too much in the way of hot weather so I've never found a problem with engine bay temperatures !
But because you've got a different engine, I think it's just a case of making sure the transfer pipes & radiators are clear, watch out for air-locks in the heater pipework and then just seeing how it goes. There's a lot of space around the engine and you could always line the rear deck lid with aluminium foil and pull out the mesh grilles if it looks like getting too hot.
As for as the rotary itself, I wouldn't get too hung up about it, after all the engine worked well enough for Mazda to sell thousands of them to people who would just get in and drive. So providing you have a similar heat transfer area, the same or greater volume of coolant, then I think you should get along fine. If the water pump isn't up to the job of pushing the water along the extended pipework then maybe an electric one in the circuit would speed up circulation, but I'd see how it runs first.
Brian
ps - good to hear that other British car you've got is up and running. Just think, if us Brits didn't send over all these unreliable cars to you guys, you'd have nothing to play with in the garage