It looks like your phone is been under the control of a virus. It must have played with your initial settings and now, things are not working the way it should have.
To get it back to its original proper stage, you can try these following:
Remove unnecessary apps
From your apps list, remove all the unnecessary apps, that are not being used everyday. You can re-install them, at any point of time later. But make sure you don't remove any in-built apps.
Disable Auto Update
From your Settings, go to the Enable/Disable Updates, and disable auto-update feature. Make sure to choose the "ask before updating" feature for this.
Disable the Google Search Widget
From your Settings, go to the Preferences, Select the Widgets. There you can scroll through them, and find the Google Search Widget. Remove that widget for the time being. You can always bring it back to your homepage afterwards, once your phone is working fine.
Run a Good Antivirus
Scan your system with a good antivirus and fix it, if it shows any threat. Once done, you need to reboot your phone and see if it works.
Even was facing a lot of issues with my phone a few days back. Finally I had to go for the factory reset formula to get my phone back to normal. But each phone has its own way of reset. So, search for the right method of factory reset and then go ahead. Don't forget to back up your data, contacts and important files, before you do so, as once you go for a factory reset, you won't be able to retrieve them back.
This may take some time, but your phone is more likely to go back to the earlier state.
Hope that works.