The Gmail thing might very well be a Gmail problem that can only be handled via the website from a PC.
For me, that was definitely the case.... My gmail was so mangled, that the 'inbox' never, ever, had anything in it.
I found the issues to be the settings, a LOT of the settings, you have to go to every tab and verify that each setting will meet your needs...
All of my email was being sent direct to the 'Archive' folder for reasons I never knew why it happened.
That meant, the email could not be found in the Inbox, Trash, Spam.... it was just 'gone' forever.
I sent myself email from a different account with a "route trace" on it, and it was delivered and Received!
duh? WTH? that caused me a lot of stomach burn, but I finally did sleuth it out.
I really suspect your email issue has nothing to do with the phone/device you are using.
I highly suggest you install Aqua Mail to help you debug this, it is a great email tool.
* Aqua Mail - email app - Android Apps on Google Play