Only we see a water tile inside AI's culture border, should the trade route be opened. The exception is the land tile with a fort and being directly connected to the city center or through other forts.1. Tested it in WB, I can show you pictures if you like? (In the test game).
As we said earlier it is possible that Saladin has a coastal city but it isn't this one and it wouldn't be connected to his Capital.
The Archer's facing only indicates where he came from, not necessarily where he's going.
If zara decided to go for the riverside, he should not appear on that tile, which is not on his route to the riverside.
I worldbuildered in ToA to check... the 100% to trade routes isn't added, but it's a multiplier of the base 1.00trade route.
Meaning we gain 1 commerce from each trade route.
The actual yield from ToA is then 10GPP (Philo)+1.5H(bureau)+1G+5.25B+2C.
Of course trade routes value will increase over time but it isn't that strong as it obsoletes at SM of course.
Back to HG: since we'll most likely build most of it under Bureaucracy but Aqueduct pre-CS, total cost is
450/2.5+150 = 180+150 = 330H
We've already put 50H in ToA so 475 are left. The difference however is it will be complete before Bureaucracy so the cost really is
475/2 = 237.5
So the actual hammer difference is more like 100H in build cost.
3 pop is already better across the empire but then you have to factor in the extra yield from ToA in Delhi. It starts getting complicated however as we also need to consider the pop points that we won't whip in the cities.
Finally there's the odds we lose out on it which are actually high (especially if we don't whip!)
In a perfect world, I'd take both of them. I think we need to carefully make this decision.
How soon are we going to obsolete ToA? Do we want something post-SM from Liberalism? (say Biology/Electricity/Radio?)
Where did you get this formula " 450/2.5+150 = 180+150 = 330H"? I mean the 2.5 divider.
Regarding the 100% trade route income, what size of the city are you using for test? My impression is that income from the city with ToA is bigger. I might be wrong. At least it's 3C with the bureo bonus and remember the 5.25 beaker is only at 75% multiplier.

I will clarify more on this issue in the reply to dingding's post.