i thinkz it just the cold start not functioning proper hence not allowing the engine to rev up to cold start. cleaning the inside of the throttle body with carby cleaner, might do the trick
the oil pressure not going up for a second while car sputtering, is jsut hte gauge takin its time to read the oil pressure, more then likely if your gauge is doing that then it aint reading accurately anymore too, cos it is the case with mine
i jsut start my car when cold adding a bit ot throttle and she is fine! idles fine if i stab the throttle a bit while starting