I'm having iPhone 4 system problems?

My phone will start acting up every now and then. Just out of the blue it will exit out of apps (not allowing me to open), same with the internet, won't receive messages, won't send out messages, sometimes won't receive calls but allows me to call, won't delete photos, dies faster, etc. I do know i have little room for data, but i can't do anything about that if my phone isn't allowing me to delete anything.

I have done all of the following,
- Bluetooth Off
- Limited Notifications
- Push Notifications off
- Location Services off
- Manuel Mail
- Brightness adjustments
- etc.

I've contacted my carrier, version, in the past and they did something over the phone that helped briefly, but over all it still likes to act up every once in awhile. I've tried killing the battery and charging it to full before operating with it, also turning it off and back on to see if it would help and still no results. If anyone knows the answer, please do tell!

Try restoring it

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