Try the following:
Go to Menu > Settings, scroll down to Applications, swipe on right side and select All
Scroll down to and select Google Search select "Clear Data", select "Clear Cache"
Go back to All then scroll to find and select Download Manager select "Clear Data", select "Clear Cache".
Go back to Main menu, restart your phone.
Hopefully it will have fixed both your problems.
Try a hard reset. (factory reset)
Be aware that a hard reset will erase all your downloaded apps and user data. It will restore your phone to a factory default condition. It will be like when you first bought it
If you can ensure that the battery is charged before you perform a hard reset. Do not have the charger connected when you perform a hard reset.
Here is a link that shows what to do.
Be patient, it takes a few minutes to complete.