To answer your questions.
#1. It's possible yes. It can happen whether you access the email on your phone or computer. Accessing it from your phone does not necessarily make your email more vulnerable. Thats the reason for secure passwords.
#2, How would your wireless provider view your browsing history? Your communication is raw machine data, where would they access it? Add to that they would need a warrant and you would know.
If you're that worried about browsing history use a mail client or app to view your mail and it won't give a browsing history.
Yahoo Mail app: https://play.google.com/store/apps/details?id=com.yahoo.mobile.client.android.mail&hl=en
Your android already has gmail just add accounts within the app. Also you can add the widget and choose your accounts. Lots of information about multiple gmail accounts on android all over the web.
I'm not even going to touch the conspiracy theorist angle because if you go that route you wouldn't care what I said. You already have your own opinion away. But it's not as cloak and dagger and big brother as some have theorized. Yes the ones and zero's are all over the ether. But compiling them to usable identifiable data is an entirely different matter. Not as easy from a random standpoint as some would lead you to believe.
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