First, on the Android Note, can you successfully goto the web-based gmail and login to your account and see your email messages? Second, do you still have your iOS device or a computer that can access the gmail account?
The issue that you are having is most likely an individual "problem" email. Meaning, there is a message in one of your boxes that your android gmail app does not like and chokes on. It could also be an issue with the naming of one or more of the labels or sub boxes in your account. Certain OSes and apps handle filenames and naming conventions differently. For instance, old versions of Windows did not like file or folder names to contain spaces, or certain other character, or to be greater than a specified length.
It could also be an issue with a particular email sitting in your box with a certain kind of attachment.
The thing is, your android gmail app is attempting to sync your entire mailbox, that includes the trash, the other folders, and previously read and sent messages.
The best course of action is to gain access to your mailbox and systematically eliminate unnecessary messages that don't need to be pulled down to your phone. Also, I would go to the sync settings and turn OFF everything else BUT the gmail.....just to eliminate any other interactions. Solve one problem at a time. Pare the problem down to as little as possible to deal with and go from there.
I can almost guarantee you that if you could dump all the messages in your mailbox and add a few new ones, they would sync just fine.
Good luck. Please report if this actually works for you.