oil pressure sensor is frequent problem on 300zx, mine would do the same.
Just changed it or install an aftermarket one.
Every car have a 'cold start' function. A valve give it more air so it idle higher for 1 or 2 min. It should be idling at 850 rpm when hot if its not, something else is wrong.
Buy yourself an Shop manual for your 300zx , you will need it
