There are a couple of really useful comments made on an earlier posting when I got one of my Hussarettes to pose with her horse. Please see
I can't satisfactorily answer the question posed by Archduke Piccolo without a photo and that is difficult (if not impossible) in the Comments section.
Yes, we did do some firing from the flank and here is an example
Firing with the pistol was no problem as the rider had full control of the horse with the left hand.
I deliberately entitled this posting for the "Blackpowder era" meaning up to say, the American Civil War, due to the generally lengthier firearms and difficulty in loading, making all horseback activities more difficult. It seems very likely that with the easy loading, quick firing, and generally shorter weapons of the late 19th Century some of these issues were mastered. It also seems obvious that if you save your firearm till your similarly mounted enemy is only 10 feet way then there is little danger to your horse as the target looms so large and at your level - so shotguns and pistols must have been tempting if your opponent had his sword drawn!
And it was not all serious..........Hussarettes need some fun to lighten the burden of historical research