Messed external APFS

Boot into Internet Recovery Mode using Command + Option + R and run Disk Utility First Aid again to see if it will repair the volume.

One part of the message looks like one of the APFS snapshots may have issues. It might be possible to delete the APFS snapshots using the Terminal command line utility "tmutil". I have no idea how this could affect your Time Machine backups or other backup software.

Since Apple has not released the necessary APFS documentation third party utilities cannot repair an APFS volume. So if Disk Utility cannot repair the volume, then you will need to erase it and reinstall macOS or restore it from backup.

Before attempting any repairs you should make sure everything is backed up.

The Disk Utility log in your first post shows there are two snapshots. The first snapshot appears to have some issues:

Checking snapshot 1 of 2

[LINES 17-249:]

error: Cross Check : ExtentRef physical extent (0xXXXXXXX + XXX) has kind APFS_KIND_UPDATE but was not referenced previously

[LINES 250-2015:]

error: Cross Check : FSroot tree references extent (0xXXXXXXX + XXX) which is not present in the ExtentRef tree

[LINES 2016-7316:]

error: Cross Check : Mismatch between extentref entry reference count (0) and calculated fsroot entry reference count (1) for extent (0xXXXXXXX + XXX)

Use the following article as a guide to check for APFS snapshots and how to delete them using "tmutil". Make sure you are checking the correct drive volume when issuing the "tmutil" command.

https://derflounder.wordpress.com/2019/05/08/creating-managing-and-using-apple-file-system-snapshots-for-startup-drive-backups/

Verifying allocated space

warning: Overallocation Detected on Main device: (27277961+8) bitmap address (7cb0)

...

If Disk Utility still shows these errors even after repairs, then you will need to erase the physical drive.

I've seen several other threads on these forums mentioning how Disk Utility reports APFS issues and tells people to boot into Recovery Mode to repair them. In Recovery Mode Disk Utility First Aid doesn't find any APFS errors. It seems Apple is still working out the kinks with APFS and Disk Utility. We as regular users have no idea if these errors are real or not. The APFS errors mentioned in the other threads are not the same as what you've listed here. I believe your errors are real and should be addressed.

It gets stuck every time after few minutes and does not complete even after 30 hours.

Maybe it's buffer for diskutil's output gets full?

Your Disk Utility log in the original post actually mentions "too many warnings generated; suppressing subsequent ones" so it is entirely possible. If running Disk Utility First Aid multiple times doesn't shorten the list of errors, then I think you have no choice but to backup the files and erase the drive.