Is it possible for a mobile phone manufacturer (other than apple) to make their phone sync with iTunes and iCal?
Remember the Motorola ROKR? Apple did license the technology at that point in time to build an iTunes compatible phone with Motorola, before the iPhone era. The Motorola SLVR L7 was one of the other few non-Apple devices compatible with iTunes.

There was also the case of the Palm Pre which supported iTunes syncing (unlicensed), but Apple kept breaking the syncing (purposedly?) with new iTunes versions, forcing users of Palm Pre's to search for hacks to get it working again.

I think this shows that it is technically possible (even through reverse engineering), but Apple is not going to sit by and allow it. This probably is even more true nowadays, as they are fiercely protecting the iTunes/iOS eco-system.

You could also use iSync to sync contacts and calendars with many different phone models, but it has gone missing since Mac OS X Lion. Here's a hint to install it again though.

EDIT:

Found a quote from Apple regarding "non-supported" devices, which illustrates their stance:


  Apple is aware that some third-parties claim that their digital media
  players are able to sync with Apple software. However, Apple does not
  provide support for, or test for compatibility with, non-Apple digital
  media players and, because software changes over time, newer versions
  of Apple’s iTunes software may no longer provide syncing functionality
  with non-Apple digital media players.


And here's a reaction from Apple to Business Week regarding the Palm Pre:


  iTunes 8.2.1 is a free software update that provides a number of
  important bug fixes. It also disables devices falsely pretending to be
  iPods, including the Palm Pre. As we've said before, newer versions of
  Apple's iTunes software may no longer provide syncing functionality
  with unsupported digital media players.