Whether the mouse cursor is displayed on your Mac's screen or not is 
controlled by the respectively active application running on your Mac.

You can use the mouse cursor with the AJAX Remote by tapping on the 
trackpad field in the location you want it to be.

Dragging is supported by AJAX Remote, too. Yet, while that feature 
works with Mac/Windows Safari, it will not on the iPhone / iPod Touch 
for technical limitations of the that mobile version:

The iPhone / iPod Touch version of Safari will not pass on any drag 
and drop, gesture or multitouch events. Only clicks.

Best regards, 
Felix Schwarz