Regarding your questions 1) and 2): On most modern arrangers, it IS possible to play rubato and trigger a syncopated chord. How cleanly it comes off depends on the model, and also the notes recorded in the style. For more insight, search my other posts with regard to the "batching" of chord input and the "retrigger" parameter.

On some of its latest models Yamaha has included something called "free play styles" with no drum track and a very subtle rhythm to facilitate this type of play.

3) I'm not a songwriter. Heck I'm not really a musician! I have noticed chord progressions repeating but it varies from song to song. That being said, I agree with Diki that being able to record a chord progression and play it back in real time is a highly useful feature.