H codes are history codes and not currently there. I would drive the car around for a while and see if any P codes.
As for descriptions, there is a sticky on it. The AP also will give a description.
SOLD --'07 E90 335i, PTF COBB E50, HFS4, ER CP, ETS 7", AA DP, Vishnu Exhaust, DCI, ACT, Nitto Nt555
SOLD '10 E92 335i M, 6MT COBB v3, ER IC, ER CP, VRSF DP, Fuel-it st2, Mfactory LSD