Disk First Aid freezes

If you run DiskUtility from your boot drive, yes it is going to lock your HD for a bit to sort through it.

IF you boot into Recovery your HD is not mounted, and you will have the same experience as when booted into target disk mode, "trouble free" (ie = Disk First Aid runs normally on my MacBook Pro, also running 10.14; and I can run Disk First Aid on my iMac when it is in target mode (using my Powerbook). Results indicate no problems on my iMac. )

Recovery http://support.apple.com/kb/HT4718

I've had the same issue. My newer iMac (2015) does what yours did. Freezes up for a while then the results show, plus the window showing what's going on does not come down. On another iMac (2013) it acts funny too except on that one the window shows up and works properly for a bit then freezes up. Hopefully this will get fixed in 10.14.2.

checking a disk (not including repairs few or many) can take more than 15 min. it may be you don't see visual feedback your expecting to see. You can open Terminal and check partitions and disk "manually" from commandline (you need the free apple developer xcode app installed).

don't fix your disk unless you have proof it needs to be fixed. (while on microsoft they continually suggest a repairing problems when nothing is wrong by false indication: microsoft users also often end up loosing their data and re-installing from USB)

if it works don't fix it

Does it work in Safe Mode... holding SHIFT key at startup?

Ah, thanks for the report, maybe because of APFS???