I have a Formula Car running a 2000 Honda CBR 929RR, aka Fireblade. It sits transversely as in the motorbike, and I use a chain drive. I can't address issues from turning it sideways and/or running a driveshaft.
I can speak highly of the engine. I mean, it's a Honda! Remember their 1.5 liter Flat 10 Formula 1 engine from the early 1970s? They've still got it! It starts easily, idles and runs smoothly, and puts out more power than I can handle. Specs for my model are 150 crank hp (real world 137 or so) and 67 ft/lbs of torque. Max HP at 10,500 rpm, redline at 11,500, and peak torque around 9K.
My car is race only. I run the stock oil system, which includes the Honda oil-water oil cooler. I don't have oiling issues (that I know of). I run a big Fluidyne radiator but no fan so my cooling isn't comparable.
Suzuki engines are the most powerful and popular. Bike engines are impressive and tend to get revamped every two years, so current 1-liter engines put out about 180 hp. (Yup! Wow.) Hondas are less popular for racing than Kawasaki or Suzuki, but I don't know if there is any reason for that.
There's lots of bike engine information at
and dsrforum.yuku.com (aka SportsRacerNet)
I've seen Chris Fiaccone's car after Brandon bought it and was totally impressed. His motor is a bit older and may not be Fuel Injected. I have some photos of his setup.
PM me if I can help more.