Anyone else got a buggy Safari and apps not updating automatically?

Which version of iOS are you using? 10.1.1?

I find apps only tend to auto-update when connected to power and WiFi. Otherwise I have to start the process manually when using the App Store.

Mine does automatically update at all since IOS 10 update

You mean it doesn't update?

Try a backup, erase, restore. Very easy if you use iCloud backup.