Did knights use crossbows from horseback? How did they compress to lances and firearms?
I'm sure this happened at some point, but it would have been rather rare. Crossbows tended to be a very specialized bit of technology, which required both the outlay for the equipment and the training involved, so you tended to see mounted crossbowmen as a separate group of professionals, usually foreign mercenaries, and even then they mostly dismounted and fought on foot, because you couldn't really reload a crossbow from the saddle. Moreover, crossbows of a standard that could actually be used effectively on late Medieval battlefields usually required two hands to operate, which made handling a horse rather difficult.
When it comes to wielding ranged weaponry, knights tended to go with what was convenient to use from the saddle. Thus, for example, during the Early to High Middle Ages, you get a good deal of knights using javelins and other thrown spears from horseback (hence why you see so many Norman knights using them in the Bayeux Tapestry), because they were similar to other equipment that was being used, could be used hand-to-hand as well as from ranged, and were easy to carry and use from the saddle.
When you get from the Late Middle Ages to the Early Modern period, you really start to see knights and men-at-arms using firearms from the saddle - they used them much more commonly on the ground for several centuries earlier - once the wheellock pistol becomes popularized in the 16th century. The advantage of the wheellock was that it could be loaded and primed to fire ahead of time and then used whenever the user desired, as opposed to the matchlock, which required a smouldering match to be kept at a constant state of readiness. The wheellock pistol was also a lot smaller and could be used with only one hand, allowing a knight or man-at-arms to keep the other hand free for a lance, a sword or other hand weapon, or indeed, the reins.
