Hi Felix.
...min aircraft requirement in order to do an IMC/IR(R)...
Theoretically, you could do an IR(R)/IMC in an aircraft with a limited panel, and just one navaid, such as VOR, or ADF.
Personally I wouldn't teach IR(R)/IMC with anything less than a full six instrument panel with redundant systems, VOR/ILS, ADF, DME, and XPDR. with at least modes A+C.
If you want an IR(R)/IMC that you can use in any practical sense, you need all those.
Can I do it if the engine is 'on condition'?
Yes.
MJ