Several apps aren't running // Google Play issues

Some apps suddenly stopped working - a notice appears saying "App won't run while Google Play Services are updating" - but nothing is updating and it's been like that for a couple of days.

There had been this regular notification, saying an app needs access to Google or something, that was the first thing that appeared, however it never allowed me to login in and connect anyway.

I also had to uninstall Google Play Store as when I opened it the screen went crazy/flashing black and white. So how can I reinstall that?