Is there a way to control the keys for the arpegiator? I presume it follows the project?

Control the keys for the arpegiator? Hmm...I wish I knew what that means... 

I read this as "constrain to scale / key".  I used to do this with a MIDI FX followed by a virtual MIDI cable.  Let me report back after I check the process in X2.

My question means, if I use the arpeggiator and hold an E key down on the keyboard that will be the lower root note, but what if I'm playing the key of D... then it should arp an Em7 right? Does the Arpegiator follow the project Key? Does it follow the key set in piano roll view for which lines are gray?

the arps are patterns that aren't key related.  the patterns typically won't stay in key.  a way to see that is to take a midi clip with the arpeggiator on and bounce it to a new clip.  the arpeggiator turns off and the generated notes are now in the prv.  if you're using shapes on the other hand, you could hold down an Em7 chord and it would arpeggiate only through the notes of the chord. 

Thanks, samptooth... I'm not sure how to use the arp to good effect if it doesn't follow key... other than use shapes of course.

You could use the pitch offset parameter to shift the key, but it's something you have to do manually.  It can be automated in the track automation, I think.

Yeah, I think the arpeggiator has a few missed opportunities. For example the guitar patterns are pretty good and could be lot more useful if there was a way to switch the patterns between major, minor and other chord types. Restraining to a key would help with the maj and minor but not if you want, say, a Sus 4 chord, or a chord that is not built on that scale. To do this you would need something like Music labs chord detection used on their "real" instrument series.