Some Apps not woking in cellular Data
I realize this is a pretty basic answer, and you might have already tried this, but have you tried uninstalling and reinstalling those apps? Even if it's saying "check your internet connection", sometimes error messages don't reflect the real problem. Those apps you mentioned (Gmail, YouTube, and Google Play Store) all come from the same developer. If this problem just started recently, it could be a glitch in a recent update. 

Alternatively, are you sure that you're logged in to those apps? The apps you mentioned are all dependent on your being properly signed in to your main Google account, via your device's accounts settings. If you've inadvertently logged out or deleted your Google account login, you'll lose access to those accounts.

Of course, if you haven't done this already, try restarting your device (turn it on and off). No joke, that actually fixes a lot of problems. :-)