Would the techniques have been used by Milites? Would they have been usable from horseback? How would they be changed if they were used from horseback? How would having a shield (like a thureos) strapped on to the offarm have affected fighting with the techniques shown in the I:33?

Since the swords depicted are similiar to a Byzantine Spathion would the Byzantine have used techniques like the ones depicted in the I:33?

The techniques of sword and buckler combat would certainly have been used by men of the knightly class, but this was not a fully-armored form, it was largely a method of unarmored street fighting. It could have been used by lower-class troops in partial armor, of course; many of them carried bucklers.

It would never be used on horseback, and it would never be performed with the buckler strapped to the arm.

I don't know anything about Byzantine weapons, but the Krakow Gladiatoria manual has an image of two fighters with messers and hungarian shields, standing in fifth and sixth ward almost exactly how I interpret them from I.33. The shields are strappedto the upper arm and then gripped in the hand.

That said, I think that these shields would seriously hamper my ability to execute the most interesting plays from I.33.

A one-handed sword shaped like a cross. (cruciform = in the form of a cross)

That is to say, your typical European sword with a long straight blade and a cross guard perpendicular to the blade. Not a curved blade like a katana or a straight blade with no real cross guard like a Roman gladius.