There are many options to pay for email, fastmail just for one. Do you use one of them?
Google isn't just an e-mail service, really.
But… you don’t really have to use Gmail to use most of Google’s other products, just as you don’t really have to use (actively) Google+ to use other Google products either.
But imagine you use an Android phone, for instance. There's a whole bunch of integrated stuff that works well together that wouldn't if you had a Google account and then kept your e-mail somewhere else. It's not really a 1:1 comparison.
Unfortunately no. You are going to be tracked whereever you go and it has GA. The reason why Google can stop reading your emails is because they have a global network now that can track you better.
And how exactly will I escape Google's data collection when Fastmail uses GA for analytics?