In such a situation, I first suggest removing the updates to the Play Store application.
Menu > Settings> Apps > All > Google Play Store > Uninstall Updates
Once this is done, access Google Play Store, it will update automatically, now see if the issues are still there. If they are, I suggest performing a Factory Data Reset to clear out any issues with the device.
Menu > Settings > Backup & Reset > Factory Data Reset
Be sure to backup any data first.
