How do Time Machine's checksums work?
I have a partial answer to my own question: while I don’t know whether Time Machine ever automatically verifies the checksums, a post on ycombinator.com provided me with an answer to my other two questions. The checksumming algorithm is the same one as the default one used by the Terminal utility cksum. The checksum values are stored in the Time Machine backup as an extended attribute of each file (com.apple.finder.copy.source.checksum#N). So to list the files for which no checksum is available, you would search for all files in the latest backup without the attribute, using a Terminal command like this one:

find '/Volumes/Time Machine HD/Backups.backupdb/Mac/Latest' -type f -not -exec xattr -x -p 'com.apple.finder.copy.source.checksum#N' '{}' ';' -print 2&gt;/dev/null | grep /


I’ll quote the original post for details on checking the stored checksum against the output of cksum:


  RJIb8RBYxzAMX9u on Apr 18, 2017
  [...] In any case, the "hash" appears to be CRC32, stored in extended attributes:

$ xattr .inputrc
com.apple.finder.copy.source.checksum#N
com.apple.metadata:_kTimeMachineNewestSnapshot
com.apple.metadata:_kTimeMachineOldestSnapshot
$ xattr -px 'com.apple.finder.copy.source.checksum#N' .inputrc
26 E5 4A AB
$ cksum .inputrc
2873812262 65 .inputrc
$ printf '%x\n' "$(cksum .inputrc | cut -d ' ' -f 1)"
ab4ae526