I recommend that you remove your drive to change the impeller, but you can do it without removing the drive (you'll be working on your back up into the drive).
The impeller is at the bottom of the upper gear case, and the lower unit has to come off to get to it. If the drive is still connected to the boat, then the impeller shaft won't spin once you put it back into the gear case. If you remove the drive, then you can spin that shaft with some effort (probably have to spin it from the ball gear though).
I'm not sure what you're asking about water shooting. I get a slight tell tale stream from the pivot caps when I'm running on the hose, but I find the Stringers to be kinda' messy with water. Once it's in the lake though, I get some bubbling behind the boat from the exhaust and that's it. I can't think of any time I've had water shooting "feet" in any direction.