Will Bridge show thumbnail previews for Illustrator files

I'll start with your last question:

This sounds like you've not given Bridge permission for Apple's protection. Simply, this is an Apple protection issue, not Adobe's issue. 

Go into the System Preferences and select the Privacy & Security tab on the left. Note that there are two options on the right you'll need to deal with: "Files and Folders," and "Full Disk Access."

First, going into Files and Folders, note that in various years of different releases of Adobe Bridge, different needs are needed. I do not know why this is, but it's always better to check and make sure that just because you did it for one release, you may or may not need it for a subsequent release.

Lastly, go into the Full Disk Access option. If you do not see your application in the list, click on the "+" symbol at the very bottom of the window. This will bring up a standard Finder window. Navigate to your Applications Folder, find Adobe Bridge, and add it to the list (You will need to add your Administrator's password to do this.). Then you can "switch" it to the "ON" position. 

This should solve your problem.

Please let us know if that works or not.

Now, with the Illustrator files: two-part answer. Some Illustrator files do not show up, I'm not sure why. All of mine do but others, not so much.

One posibility is that when they saved them, they did not turn on the option to also have a PDF compatible file (see below)

If I recall correctly, if you do not have this checked, it will not show up in Bridge. If you do not have it checked, it WILL NOT show up when tap the Space Bar on the Mac. In Bridge, currently, if you not have this checked, the file that shows up will be smaller.

However, if you do check this option, the file size may be larger.

I hope this all helps.