Almost certain your water pump is on it's way out--mine did the same thing for a couple weeks before going out. Your idling thing could be related to that--sounds weird but if faults(not codes) are being stored because of pump other things can act weird. I posted a thread a month ago relating to this and how my transmission was acting up due to water pump failure.
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2013 335i Msport Black sapphire/Coral red. MHD. stage 2--e30 VRSF DP, ER CP, Dinan Shockware. VRSF 12mm/15mm spacers. Cobra dashcam. Various codings.
Last car: 2011 335i Msport. JB4. Vrsf CP
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