My team ran a Turbo-Dodge at the first few ChunpCar events. It was an 87 Shelby CSX that was legitimately bought off Craigslist after the owner got frustrated with it and drove over it with his off-road truck.
We had no real engine-related reliability issues. It helped that we freshened the engine before the first event. We did spit a rocker arm off. Twice. Whic was due to an overzealous driver who over-revved the engine. Twice.
We did have transmission issues, again likely due to the overzealous driver and also the age of the components. We put a slightly used sintered iron disc setup in it that cracked in half and caused us to DNF with 30 minutes to go at the very first ChumpCar event :/. That was frustrating to say the least. We also suffered from a lot of inside wheelspin, which doesn't help the longevity of the transaxle. If I were to do it again, I'd weld the diff (it's not ideal, but it's cheap racing, so limited slips aren't really in the budget). Which makes the car much more of a point/shoot and requires more rear seat bar/roll stiffness to get it to rotate.
The engine was prepared with a port matched water pump and oil pump housings/block ports. We added a coolant bypass from the top of the water pump housing to the end of the cylinder head to help provide even cooling. We used a cross-drilled block and head with a Mopar Performance head gasket and headbolts.
Turbo was a stock Garrett, just freshened up with a new center section and balanced. At those boost levels and with the larger intercooler, I might have gone with the smaller Mitsubishi since it spools so much quicker, combined with a welded diff it would have made corner exit much more fun at the expense of ultimate top speed.
On the bottom end, it was stock with a crank-scraper and a baffled oil pan (fabricated ourselves from scrap).
We added an external oil cooler and a large intercooler (from a Volvo maybe?) and kept the boost level around stock with a mechanical boost controller (Grainger valve). We also vented the hood to help improve cooling.
Engine mounts and bushings were from PolyBushings.com (he was a local supporter so we put his decals on the car and we got free shipping/delivery).
Exhaust was 2.5" with a turbo style muffler, exiting out the driver's side in front of the rear wheel. Worked well and was cheap/lightweight. We didn't have any noise issues and it wasn't annoying in the car with the window open, but it had that characteristic "old power boat" noise that they are famous for.
The vacuum lines were simplified using a vacuum distribution block and fresh silicone vacuum lines and press lock fittings where possible. Electrical was stock, but excess wires were removed to simplify things and questionable wiring or connectors were replaced as they are easily damaged due to age and heat.
For handling we adapted take off Subaru STi front struts and springs by using the Subaru top hats and cutting and welding the strut towers to fit them. The result was a lowered front end with plenty of travel and much, much stiffer. The rear had a sway bar fabricated from flat steel stock to plate the center bar and held in place with exhaust clamps to allow for adjustment or removal depending on weather conditions (it was Halloween in portland, Oregon, so rain was forecast).
Brakes were 11" Daytona R/T units front and rear with braided lines and Stop-Tech pads.
We ran as high as 4th in our first race, and it was consistently quick and didn't have any handling issues other than the inside wheel spin, so it was a momentum car that had warp speed once the wheels were straightened.