Large files having neither checksum is due to the maximum size limit, which can be changed under Preferences / Miscellaneous / Advanced [Limits]: max_md5_file_size.
You can set it to 0 if you want to remove the limit entirely, but that can mean huge files trigger lengthy hash calculations in the main file display, when you don't want them to, so it's not always a good idea.
(Manually triggering the calculation, via Edit > Calculate [MD5|SHA-1] Checksums, can also be used to bypass the limit, but doesn't affect Print Folder.)
That said, in the next update, we'll make it so Print/Export Folder ignores the size limit entirely. If you're exporting that data, you probably always want it to be calculated in full, so we'll make that change.
The other issue, where only one of the two checksums appears in the Print/Export Folder output, is a bug. We've fixed that for the next update. Many thanks for reporting it!