About edges that break easily http://www.thearma.org/essays/edgemyth.htm.
It happens only if you fight like a wild boar (like often I do myself) and not like a skilled swordman.
Who is the master of fencing you learned with? Where did he study? Take care: there are many "masters" that have a great passion for sure, but little real knowledge. Since there's no more a direct tradition from middle-ages, a proper interpretation of ancient treatises is crucial in reviving the Art, and usually only academic studies, or the teachings of a well-known association, allow a proper understanding of the secrets of ancient masters, who often wrote using a quite cryptic language exactly to confuse casual readers.
P.S.
(I study medieval archeology, btw, not physics)
(I assume when you speak about german armor you are referring to the so called "gothic plate": if so it's late XV, not XIII)
EDIT:Correct: the first iconographic example AFAIK is in the tapestry of Bayeux, depicting normans using it vs. Saxons; there's a problem here: the couched lance is an anti-cavalry technique, useful to brutally dismount enemy knights (and eventually kill them), but in the tapestry is used against infantry... Probably an error of the author...
About the shield, the iron mail often was not enough to protect from the weapons of the age, it was very effective against non-bodkin arrows, but even a strong sword cut sometimes was enough to seriously injure the wearer, so the shield was still very important.
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