I've tested an iPhone 5 in the car.
It acted strangely the first time I did a bluetooth pairing...had to restart the phone and un-pair, then try again. Then all good.
The key to making sure that your messages show up is both the set-up on your BMW-side, and the iPhone's "notifications" for Messages. I toggled the "View in Lock Screen" and it definitely does NOT send messages to your BMW if you have this off.
Attached is a screen print of my settings in "Notifications...Messages."
Also, it does take a moment for the car and iPhone to sync stuff, on the first time. So don't be in too much of a rush... give it a full minute to catch up to what you're doing.
Incidentally, as noted on another posting, I tried the included-in-the-box Lighting-to-USB cable, and all of the Connected Drive stuff DOES work.