iPhone 5s - apps, contacts, calendar, and ... don't synch from iMac
Just found this which points to part of the answer:

http://www.macworld.com/article/2057971/sync-contacts-and-calendars-with-your-iphone-via-itunes-not-in-mavericks-you-dont.html

Sync contacts and calendars with your iPhone via iTunes? Not in Mavericks you don't

There may be more than 200 new feature in OS X Mavericks, the latest version of the Mac OS. But while Apple giveth it also taketh away: The ability to sync contact and calendars stored locally on your Mac with an iOS device is gone.

...

Is this an insidious plot to get everyone to use iCloud for syncing? Well yes, sort of. A tech note on Apple’s website explains:

 If you use OS X Mavericks v.10.9 or later, your contacts, calendars, and other info are updated on your computers and iOS devices via iCloud.


So there you have it.