I have to assume we have horses nearby - it seems odd to think a civ with a chariot UU wouldn't be able to build them until the MA - or can 3-man chariots be built even after horse back riding shows up?
I think so. From memory the Civpedia says they upgrade to Knights, I am playing the Mesopotamia scenario at the moment with the Hittites, the UU has a defence of 2 so is the best choice til swordsmen are an option. Then it's speed vs attack. Regardless I like to build plenty of seige units to go with my forces. What you build will really depend on how close aggressive our neighbours are.
Not necessarily I think Babylonian bowmen get a worse defence when they upgrade to longbows (only 1).I believe so. They cost the same as Horsemen, but get the '2' defense.