Sounds like you either have apps that are running in the background and accessing your data, without realizing it, or you have something unwanted on the device. Bad app, virus, malware, etc.
With it acting this bad, I would really suggest you back up all your personal stuff to a computer or other location off of the device. We are talking photos, files, music, contacts, bookmarks, etc. Just not apps, you can't back them up. However you can sometimes back up their data. Depends on the app.
Once you have backed everything up to a location off the phone, then do a "Hard Reset" of the phone. Instructions below.
This will reset the device to its original state, prior to use. You can then go and set it up again, how you want it to be. However, before starting that, I would suggest uninstalling any apps that are preinstalled and you don't want/use, and for those it won't allow you to uninstall, that you disable them. Then they won't bother you later.
Do this and then install your other stuff. Do make sure to keep a backup off of the device, just in case. Then, when you install your new apps, go into their settings (including your google and google play store settings) and make sure they are not set to auto access the internet or auto download anything. You may even, after all that is done, want to go into the phone's "Settings" and turn off data when you are not using it. Just remember it isn't just for online access or apps, but that any messages (through the messaging app) with any images, etc., also use data.
NOTE: Doing this will clear 'all' the data on your phone, so it is suggested you not choose this option unless you have to, or aren't worried about losing anything on the device.
Be sure you back up any data you want to keep, to a computer or cloud account, before doing the reset.
To "Hard Reset" the phone...
1. Make sure that the phone is actually powered off.
2. Remove your SD card, if there is one in the device.
3. Press the "Power" and the "Volume Up" buttons, together, until you see the start-up logo on the screen.
4. Once you can see the logo, release the buttons and allow the device to enter the "System Recovery Mode".
5. Next use "Volume Down" button to get to the "wipe data/factory reset" option.
6. When in recovery mode the "Volume Up" and "Volume Down" buttons are how to can navigate and highlight what option you need.
7. Once you have selected the "wipe data/factory reset", press the "Power" button to select that option.
8. On the following screen, repeatedly press the "Volume Down" button until the "Yes - delete all user data" option is what is selected.
9. Then press the "Power" button to hard reset the phone.
10. If you took your SD card out in step 2, when the device is up and running again, reinsert the SD card.