Using Migration Assistant

Nothing will be removed from the old Mac Mini when you migrate to the new Mac Mini.

Do you mean something like File Sharing and Screen Sharing between the two Mac Mini's?

https://support.apple.com/guide/mac-help/set-up-file-sharing-on-mac-mh17131/10.14/mac/10.14

https://support.apple.com/guide/mac-help/turn-screen-sharing-on-or-off-mh11848/10.14/mac/10.14

Yes, it can (https://support.apple.com/en-ie/guide/mac-help/mh19569/mac) but I would not recommend it in your case. I gathered from your messages that you want to protect your old Mac Mini data as much as possible. You would have to turn on the old Mac Mini to access its DVD, meaning that the hard-drive of the old Mac would be spinning every time you turn it on. The more a hard-rive is used, the more likely it will fail and if it fails you loose all your data on the old Mac Mini.

The preferred solution is to buy a dedicated DVD drive for the new Mac Mini. You can find them for $25 or so (Best Buy has an LG DVD for $24.99, for instance). This is very little money for peace of mind.

You are welcome. One last thing I need to mention: Time Machine. If you intend to use the same backup drive for the new Mac Mini, turn off Time Machine on the old Mac Mini once you have completed the migration. You don't want Time Machine to kick in if you turn on the old Mac Mini; this could potentially cause unwanted side effects on the backups of the new Mac Mini.

SteveH wrote:

So, is Migrating the same as copying?

Yes

We want to be able to save all our old emails on the old Mini Mac (which will be totally disconnected), while Migrating all our settings, data files, Firefox (bookmarks) & Ttunderbird Profiles over to a new Mojave Mac Mini.

Yes that will work no problem.

But keep in mind, that a new 2018 Intel Mac Mini and the new M1 Mac Mini will come with Big Sur and will not be able to run Mojave. The only way to run Mojave or Catalina, would be on an earlier 2012-2014 or to get an older used 2018 Mac Mini.

Yes, it is. Every stays on the old Mac and is copied to the new Mac. Also, make sure not to remove your email accounts from the old min as it will delete your emails.

Yes, everything will be left intact on the old Mac Mini.