Depends on what you mean by read. The contents of your email are processed by algorithms and those algorithms are used for advertising purposes. Google employees aren't reading your email.
Yes, it is spam filtered, tagged, categorized, most likely the meta data is utilized somewhere to enumerate your friends, business partners, and so on. Officially though, the content is not used for advertising purposes.
I see this repeated a lot and the reasoning doesn't hold up. You aren't the product - your data is a commodity. And there's plenty of free stuff online for which your data isn't a commodity (e.g. Wikipedia, Project Gutenberg, Khan Academy, so much of the free and open source software). So saying something like "if it's free, you're the product" is just lazy and demonstrably false.
That's not a great comparison. The free stuff like Wikipedia is supported through donations. In theory, if you're using it then you should also be donating a little to it.
I think if you are using a service/site run by a for-profit company, then it's probably fair to assume that they are making money off you somehow.
I mean, that's not as clear cut. There would be nothing stopping them from reading the contents of your mail or playing fast and loose with your data even if you were a paying customer. It's not a zero-sum game, as long as there is money to be made you rely on the goodness of their heart to not pursue it.
