However the Bablonian UU is good.
I don't think it's good compared to Skirmisher, at least in single player, because:
Defending a city/hill/forest/jungle against a Melee unit:
Bowman (no fortify): 3*(1,00+0,50+0,50)=6,00 (+1fs)
Bowman (25% fortify): 3*(1,00+0,50+0,50+0,25)=6,75 (+1fs)
Skirmisher (no fortify): 4*(1,00+0,50)=6,00 (+1-2fs)
Skirmisher (25% fortify): 4*(1,00+0,50+0,25)=7,00 (+1-2fs)
Defending a city on hill against a Melee unit:
Bowman (no fortify): 3*(1,00+0,50+0,50+0,50)=7,50 (+1fs)
Bowman (25% fortify): 3*(1,00+0,50+0,50+0,50+0,25)=8,25 (+1fs)
Skirmisher (no fortify): 4*(1,00+0,50+0,50)=8,00 (+1-2fs)
Skirmisher (25% fortify): 4*(1,00+0,50+0,50+0,25)=9,00 (+1-2fs)
Defending on field against a Melee unit:
Bowman (no fortify): 3*(1,00+0,50)=4,50 (+1fs), not enough against an Axeman or a Swordsman
Bowman (25% fortify): 3*(1,00+0,50+0,25)=5,25 (+1fs), not enough against a Swordsman
Skirmisher (no fortify): 4*(1,00)=4,00 (+1-2fs), not enough against an Axeman or a Swordsman
Skirmisher (25% fortify): 4*(1,00+0,25)=5,00 (+1-2fs), not enough against a Swordsman
So in short, Bowmen are better than Skirmisher only when defending on field against a Melee unit or when attacking against a Melee unit, but these many times lead to Bowman's death still.
Note: I haven't seen many AI CR2/CR3-promoted Melee units, so these numbers are against Combat-promoted Melee units (Combats effect the unit that has them, while City Raiders effect the defender as a minus).
Also, promotions effect higher base strength better (when defending).
The Odeon's not really all that good. I mean, first of all, you might as well forget about the extra happiness from hit singles, because that happens soooo late in the game. +3 culture is nice, but it's hardly unbalanced. and 2 artists? Why on earth would you want to run artists? Give me scientists and engineers any day.
When I'm running Representation and have built Academies in my main research cities, I usually like Artists more than Scientists. 4 research and 4 culture beats 6 research in my opinion. I like cultural victories very much though.
The only reason for Priest Specialist is Great Prophet, which is very dubious.
Not true. With Angkor Wat, Priests give 2 hammers and 1 gold, which makes getting Great Engineers and rush-wonders only reason to assign an Engineer if you can assign a Priest, and settled Great Prophets are just great, while not as great as settled Great Merchants. I would still leave Angkor Wat and run other specialists than Engineers and Priests.