Looks that way
Just a couple more things.
- settings - security - device administrators. What is it checked in there?
- Are you using any battery booster, cleaner app or RAM optimizer? If so, disable them or even uninstall. I've seen some people having very funny issues with this kind of apps.
- You are using the stock launcher, right? Would you like trying a custom one and see if anything changes? Some of your issues seem launcher related. Nova would be my first option.
I'm running from place to place today

I'll let you know if I find something else later on.