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Go to settings-apps-all,scroll down until you find chrome,it should be disabled.
You should get in google play and try to update/download from there.See if that helps.
If you boot the phone in safe mode,how is it?
talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008
Yes,by factory reset you should get them all at their primary state(default).Good,keep us updated and do not worry,we are here to help in any case we can.
You can use Pc companion to backup your messages,contacts,settings or backup on google servers.Media files should be manually copied on your PC or laptop,because they might be too much for the backup and it might freeze.