Should developers make links to external sites open in a new tab?

Depends on your audience. If your audience is techie enough to know opening in a new tab or holding Ctrl/Cmd before clicking, don't bother.

Also, always add rel="noopener" to such links.

I don't let external links open in a new tab, so the user can choose the prefered behaviour.

No, from my experience. Opening a new tab breaks the web history journey. Most people Ctrl/Cmd click or right click open.

yes, in my opinion. No downside in making sure your website maintains a tab in the users browser while they browse other sites.

Not necessarily. I always do that myself.