a. Normans 100% did use combined arms as their tactics of choice. Look at Hastings. They have a whole army built up on combined arms tactics with archers, infantry and cavalry operating in support. The one exception is Civitate, because the Normans were hungry, starved and desperate and really didn't have a lot of troops left for a combined arms battle.

b. North european normans did not use couched lances as a standard tactic by the battle of Hastings. Take a look at the Bayeaux tapestry and look at how they're holding their lances (or read any account of the battle). This means that the practice was not widely used by the normans under William I, but was known and popular among the normans following the battle of Manzikert (because we have accounts of Michael VII training byzantine cavalry in the "european style". "Latinkon" however, units equipped and trained specificly to emulate european cavalry, did not appear until Manuel I).

c. The massed charge using couched lances was probably invented by the persians, and it was known by the East romans and probably used by Nikephoros Phokas (the elder) as the technique appears among East roman ally states like the Georgians (who most likely learned the technique during the Cilician campaign of 964. There are a number of military accounts, for example accounts of the Georgian-Seljuk wars, as well as georgian art that depicts riders using couched lances). Note that it's likely that the georgians did not use heavy shock cavalry, as georgian shock cavalry developed out of a tradition of horse archers (so, smaller horses bred for endurance rather than size, weight and shock).

The main reason for East romans not using shock cavalry techniques as standard lies in attitude, equipment and the enemies they faced. 1. The enemies East Rome faced were disciplined and more well trained than most italian infantry, blunting the efficiency of a massed charge. 2. East roman cavalry (kataphraktoi) used much heavier armor and we see no sign of destriers. 3. East Roman battle tactics in the 11th century favored a much more defensive style than the italo-normans.

In short. The normans took a technique that was known, but not favored, by the east romans. Decided they liked it and gradually became more and more specialized in gear and attitude towards favoring that tactic. It's the same kind of "combined arms devolution" that we see after Alexander (where we see a combined arms army devolving into the successor state army that heavily favors big blocks of pikes).

P.S: Note that all of the east roman ally states that took up shock cavalry tactics in the 10th and 11th century were what the East romans would have considered cavalry of lesser status. Light&medium supporting cavalry. Which means no barding or costly (and heavy) laminar armor.