The ECU does not monitor oil pressure, and it has own coolant temperature sending unit, separate from the one that feeds the gauge in the dash.
Basically, you can separate the engine and ECU from the rest of the car with minimal electrical drama. It will not by physically easy, because the engine does not have a separate harness, but the ECU doesn't need anything from the car other than constant power, switched power, and ground. All its other critical inputs and outputs are directly related to the engine or fuel injection (i.e. pump, relay, etc).
Your project sounds really interesting. Are you following a set of plans or just designing the whole thing from scratch? These two look like a hell of a lot of fun to me:
http://www.grabercars.com/
Sylva Riot SE