Using Migration assistant

The case sensitive format like your old Mac means that a file named BigText and one named bigtest are handled as different files. However, with case insensitive like your new Mac those two files would be treated as being the same. Thus if you migrate they can be what the new Mac determined to be two files with the same name and get a collision.

Possible solutions:

1. Manually copy files from old to new
2. Make a Time Machine backup and restore your old Mac from that TM backup. If when restoring you will get messages if two there would be a collision for two files on the old Mac that only differ by capitalization. See

https://web.archive.org/web/20150913072428/http://pondini.org/TM/E7.html

3. Erase Boot the new Mac to Recovery and format/erase the disk and format as APFS case sensitive and reinstall macOS and then migrate

About macOS Recovery - Apple Support

In the past I've seen reports and dealt with a few issues with customers where applications haven't supported the case sensitive formatted drive. Adobe is/was a big offender in this regard. Since you apparently haven't run into any problems you might be able to get away with just formatting the new Mac mini case sensitive and after installing Mojave use Setup Assistant to move data and applications.

However if it were my problem I think I'd take this as an opportunity to clean house. In other words, I'd manually install my apps on the new computer and drag data form the old computer to the new. Inconvenient perhaps but I can't think of any easy way to move from case sensitive to case insensitive. Perhaps there are backup programs other than TM that would happily copy data from your computer to an external if you'd like to try that route - and $$ buying a program that might work.

SuperDuper isn't the most polished backup tool but for this purpose it could be used in the free mode (entire drive clone). Nothing to lose other than time trying.

It depends upon the software. A lot of software only installs in the Applications folder as one blob, or maybe two. However, as dwb said, some apps install pieces in other places too.

Just copy the one in the Applications folder and see if the app works.

You can’t in many (most) cases because many applications have pieces installed in other places.

Limnos, cloning the 2011 MBP should not work since that model can only go as high as HIgh Sierra and the 2018 Mini can't run that old of macOS version.