Definitely yes to this one. Notice at the bottom of any topic email notification, there is a message “Visit Topic or reply to this email to respond.”
Yes, Discourse supports this. It even (optionally) supports starting topics from email addresses who are not already users, via something called “staged users”. However, these features would need to be enabled in the settings. It looks like the basic toggle is called “email in” and default minimum trust level is 2. But at a quick glance, I suspect configuring everything properly may be more involved than just that checkbox. I recall that @thewtex told me it was quite tricky to get all these email-related features working as desired for the ITK forum.
Personally, I would be reluctant to enable starting new topics via email because I am concerned it could bring along issues of increased spam, and therefore moderation effort. However, if you feel the potential burden would be worth it to placate the email-centric people, and want to give it a try, then please feel free to read up on how it works in more detail and do some experiments with it. I promoted you to admin just now, so there should be no technical obstacles to you doing so.