Gertrude,
In my limited experience, I'd say the practice of letting the aircraft fly itself off the runway tends to apply to tail-draggers.
And floatplanes
I don't know about that... but
I hope to find out soon! 
As for cross-winds, I thought the idea was to apply full into-wind aileron at the start of the take-off roll, and gradually decrease the aileron as you gather speed and the controls become more effective. Thus, when the wheels loose their grip, the horizontal component of the lift vector should keep you going straight down the runway. Admittedly easier in a tail-dragger... which might be why they are more often flown this way???
FFF
--------------