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Not really sure whats going on with your phone, But why not give a try to do a software repair with PC Companion?
Hi, there has been a few posts before regarding the Flaps 'popping' open whilst either just sitting on a table or even in peoples pockets!!!!! Could you lay your phone flat to check that it is not showing any sign of being flexed first? Only other thing i would suggest is to take it back to where you bought it or your nearest Xperia Care Centre.......
With regards to the screen always going to Playstore when you unlock it....try changing the way you unlock the phone, just a test to see if it still happens......try perhaps putting a PIN code in for unlocking or maybe a Pattern......
Get back to the Forum with the results,
Hope this heps:smileysmileywink: