When mounted knights armed with lances (swords, maces, etc as secondary armament) attack heavy infantry (Shield Wall / Pikemen), do they use their lances at all or is it more a matter of breaking the enemy formation with impact of his armored horse, after which he fights with his secondary weapon? Is the lance more for killing other mounted knights or isolated heavy infantry thanks to its single use nature?

The lance works to concentrate the impact of the armored horse to a single point, and to deliver that point in advance of your own body and the horse’s body (and hopefully before their spear can reach you). And lances aren’t necessarily single-use – war lances aren’t made to break like tourney lances (although given the speed of impact, it’s possible it’ll break anyway), and the main trick is A. bringing your lance back on line quickly after the first contact, because you don’t have long to do it before you hit the second rank and if they get inside the point you need to switch to your secondary weapon right now), and B. keeping a good enough grip on the lance so that if the lance sticks in someone, you pull it out of them as you ride past rather than having it pulled out of your hand.