Maybe I can be of some help here

Vasiliki Ili
What language is this? Basilikoi Illoi would be the Greek.

"("clerouchoi" is not a military term)." This was land granted for the express purpose of raising a regional army reserve and the troops so raised were called Cleruch Cavalry and Cleruch Infantry. How this is not to be considered a military term escapes me.
Well, strictly speaking, Kleruchoi is not a military term at all. Kleros is a something drawn by lot, and echo is a verb meaning have. 'Having been aportioned by lot' is the strict meaning of Kleruchoi. In Ptolemaic Egypt or Selucid Syria it would mean that the men were given land by lot in reward for service. It was used in Athens for something entirely different.

Heteroi Cavalry
Should be Hetairoi. Interestingly enough a Hetairos could also be a homosexual prostitute. 'Companion' is diverse in its meaning.

Agema Foot Guards;"In peace time and war time the seleucids had a Royal Guard that was made from both cavalry and infantry."
He's right, it should be Agemata.

There is no 'C' in Greek. Kataphraktoi, please.

The Kataphraktoi were certainly not Gallatian. Greeks probably, but not Gallatians.

Euzonoi
Generally means light infantry. It's a fine and all encompasing term. Worthy of note, there may not have been Thracians at all in the Selucid army. Anyone who was a peltast could have been called a Thracian, just as anyone who was an archer in the Cretan style could be called a Cretan Archer.

"later they included asians still fighting in the Macedonian way." These were called Pantodopoi. Levy Greeks were later called this as well.
Perfectly correct. Pantodopoi is a great term. The Asiatic troops were never of good quality.

Nestor, if your sources are in Greek, I'd be delighted to sink my teeth into them. Are they online? If not, can you give me book titles?