I had similar issues at first also. Actually the first 2 hours with my surface pro was trying to figure out how to get the dang gmail app to work. Kept getting errors.
It has something to do with how Google changed their services or something that's no longer working with outlook or like the way it use to do it. So I found a Backdoor way to set it up. Since mail app wouldn't accept my gmail, I figured let me see if the contacts will sync with gmail contacts. So I open up contacts then sync and entered in my gmail info. It worked first time. Then it told me now my gmail account is linked to Microsoft or whatever. So I go back onto mail app. Then try entering in my info again. Now it accepted it, no issues. I'm figuring it finally.worked because I got it to link in contacts. Therefore allowing the mail app to accept gmail info.
Now my.gmail works just fine. I remember researching like crazy trying different things to figure out why gmail wouldn't work initially..lol that Backdoor method worked for me. Try it.
