Google has absolutely no customer support whatsoever. I don't know anything about FastMail customer support, but it's hard to argue it's worse than no customer support.

Unless customer service means something different than customer support. What does it mean?

Personally, I use Google Apps for Business and since a few months ago Hangouts doesn't work correctly any more. It's almost unusable at times.

What can I do? Who can I complain to? How can I escalate this? Absolutely nobody can help me.

Once I figure out a feasible transition plan from Hangouts, I'm done with doing business with Google.