I get a lot of ads in my email and unsubscribing doesn't do the trick. I also get rather inappropriate emails. How do I protect my account from these?

If they are from one or several sources, go to Mail/Preferences/Rules and create a rule to delete them or move them to the Trash.

Sample below.

Clicking the unsubscribe button in spam emails is the worst thing you can do. It only tells the spammers, who don't care one whit about the law, that yours is a live email address. They then not only send you more spam, they sell your address to other spammers on a list of verified addresses.

Never, ever, click the unsubscribe button.

When ios mail detects a mailing list email, it displays a banner notification above the email with an unsubscribe option. Does that operate differently, and more securely, than clicking on the more dangerous unsubscribe link in the email itself?

I use Outlook on my Mac, but Mail on my iPad and iPhone. I have noticed that unsubscribe link, but have never looked into how that works. As you questioned, does it send an unsubscribe notice back to the sender's mail server, or is it a blacklist link that tells Apple's mail server to automatically delete all future emails from that address?

You are welcome.