Hello, I face all your same Google play problems but besides I also face a battery problem. I just get my phone 2 days before my first charge from %10 to %100 took 8 hours.
Second and third charge time is better than first one but my battey drain very fast. I read a lot of reviews that say perfect battery time but my battery gets empty quicker than my 1750mah Xperia L.
Is there anyone that faces my problem? Maybe this can be also a bug of 7.3.2 rom.