You are describing two separate problems.
Firstly, yes, when you first send a book to the Kobo devices, the size will show as zero in the device list. When you disconnect, let the device import the books and reconnected, the size should show correctly. As far as I can tell, other devices have the same problem. I have looked at fixing it, and it isn't worth it.
The bigger issue is why the books didn't get imported when you disconnected the device. The first thing to check is that the books were actually copied to the device. After sending the books, open the drive for the device in explorer, Finder or whatever and look for the books. If the files are not there, then there is an error sending them. I would need to see a debug log from the send to see why.
If the books are on the device when you eject them, they should be imported by the device. You should get the black importing screen shortly after the eject, but it can take a minute or so to appear if you have a lot of books on the device. That screen has a progress bar to show the progress.
If the import screen doesn't show, that means the device didn't see the new books. That will happen when resending books. It could mean the book wasn't copied to the device (see above). It could also mean the file name was invalid. Calibre shouldn't produce file names that the device doesn't like, but it is possible I missed a case. Also, if the file name or directory the books are in starts with a dot, then the books will be ignored. Again, calibre shouldn't let this happen, but there might be a way.
The other reason for books not to be imported is errors in the book. For some errors, the device will not import a book, and will also ignore the rest of the books in that batch. There is a discussion on this happening in the Kobo forum at the moment. That specifies an error that causes problems, but, there are other reasons. For a CBZ, it is likely that the problem is caused by the internal file names. I'd have to see one to guess.
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