As in Homeric warfare.
Having visible slots on units would be a great feature to have, also for war elephants. I believe some work was started on it, but no patches have been committed yet.
Yes, you're right, and this applies to the other civilizations as well. Horses need a lot of food and space and are only useful for travelling and warfare; only the richest people (e.g. equites in Rome, hippeis in Sparta) could afford them. In Ptolemaic Egypt, “Macedonian” phalangites held 30 or 25 arourai of land, horsemen 80 or 100.
In 0 A.D. “elite” means simply a promoted “basic” soldier, whereas “champions” are the real elite.
Again true for other civilizations as well: cavalry typically had javelins, spears, and swords; the same is true for most infantry. Differentiating units by weapon types is not really realistic, but certainly makes sense for 0 A.D. and similar games.