Q: Remote access? "other" user shows up in Excel file

"wheel" is an administer group.  It comes from the Unix world and stands for "Big Wheel" as in someone that is important, a boss, someone in control, etc...

<https://www.urbandictionary.com/define.php?term=Big+Wheel>

It is not someone getting into your system.

If you are the admin account, then your "ARE" a member of the "wheel" group, so you have the right to mess with files in the "wheel" group.  If your husband is a "Standard" user, he is not part of the "wheel" group.

Now why the file or folder your husband was trying to save a file to had "wheel" as a group owner, that is a different question, but "wheel" is not some remote user, and you have not been hacked.

With respect to firewalls, if your Mac mini is at home behind a home WiFi router (often times provided by your ISP, but it could be your own), then the Firewall is not needed, as your home router is acting as a Firewall between you and the Internet.

Again, I do not think you have been hacked, and as I've explained, "wheel" is a standard OS X group associated with Administrators.

As an example of "wheel" usage, the following is a Terminal ls -lG of the top of my file system (yours would look similar)

Notice that most of the files and directories (folders) have "wheel" as their group, and "root" as the owner (root is the most powerful account on any Unix based operating system, which is why the files and directories at the top of the file system are owned by "root").

I do know that this machine is being taxed, and we are getting ready to switch to our more powerful iMac.

I have an even older Mac mini with a basic OS X install, and it provides backups for the other systems in my home.  I've attached extra USB storage, and I run the "free" version of CrashPlan.  CrashPlan allows me to  network backup across the internet my laptop, my Wife's laptop(s), and my Mom's iMac (300 miles away).  Very useful to me when I'm away from home (such as on vacation), I'm still getting backuped.  The connections are encrypted, so nothing is going anywhere in the clear.

Just a thought for something to do with the old Mac mini.

Another thought is that maybe you have accumulated a lot of cruft over the years, and maybe some house cleaning would improve the Mac mini's performance.  If you can run Mountain Lion (10.8), you can run El Capitan on that Mac mini.  You could post the EtreCheck output and someone in the forum will most likely look at it to see if they see any thing that could be affecting your performance.

<https://discussions.apple.com/docs/DOC-6174>

Also you could run Applications -> Utilities -> Activity Monitor.  Start it, then ignore it for awhile and use your Mac mini as normal.  Then go back and look at the various tabs.  The "Energy" tab might show you apps that seem to be hogging resources and a candidate to be removed.

Also look at Applications -> Utilities -> Console and see if there are any log entries that show a process starting, dying, starting, dying, starting, ....  Sometimes a 3rd party addition add in a previous OS X release is not compatible with your current OS X release, and its start/die cycle could be draining resoruces making your system slow.