What I learned was: those rectangles to the left of the collections (on my iMac), with which to mark a collection to be synced, appear only once the START commend is clicked (and accepted) above the name plate. Then the rectangles disappear from other computers (e.g. my MacBook).
Correct. You can only have
one synced catalogue, so when you start sync in a catalogue "the rectangles disappear from other
computers catalogues".
What remains mysterious: while I had known that only one catalog can be synced to a LR Mobile at any one time, I don't have a clue how the images initially synced to LR Mobile got there - it seems from my iPhone. But then why were the rectangles showing on LR CC on my MacBook? The MacBook didn't have any collections and also no images. And why did it take a total of two days to finally delete those initially synced images?
They were showing because
you must have inadvertently started Sync in the catalogue on your MacBook. To be kind, I'm not sure I trust your explanation of how you got things into the state they were in
I won't give the mysteries any more thought. Syncing now seems to work (as intended). I don't have an odd LR CC version. I don't plan on processing images on my iPad, they're for viewing only.
Showing pictures and after reviewing them (adding stars and flags) have always been my main LrM activities, and processing them has come third. It's not for fine tuning - the screen isn't even calibrated - but it's fine for ball park adjustments that mean your time at the desk can then be devoted to fine tuning.
Do look at lightroom.adobe.com again. If you're on your MacBook, it lets you use your browser to see pictures synced up from the synced catalogue that's on your iMac and download JPEG versions. You can do some adjustments, flags and ratings, add titles and captions. Also let's say you create something on your MacBook, you can drag the file from Finder and drop it into the browser - this uploads it to LrMobile and the file will subsequently appear in your synced catalogue and be downloaded to your iMac. That can be very convenient.
John