if you do a long press on the title of the book you want to delete while on library/shelf you'll have the option to delete it (idk about the syncing, i've never done that and I only have 1 device). same for tiles, though i have no recommendations tile so idk if that's one like the "sync" tile that one can't dismiss? (the dismiss is temporary, iirc)
also if you go to settings>reading life and notifications you can uncheck the kobo notification option (not sure that's what you wanted, but less push from kobo is better).
maybe others with more than 1 kobo device will help you more
