Ads in Gmail are not related to your emails: https://support.google.com/mail/answer/6603
Google still saves and parses every email it gets and likely uses that data for a number of purposes. No longer directly targeting Gmail ads with it really doesn't do much for people who are concerned about Google and privacy issues.
Sure, but so does literally every email provider. Storing your email and spam classification are pretty much the two biggest features an email provider can provide.
This is like objections to "algorithms" or "chemicals".