Okay, not sure why we were researching Sailing at this point, but that's by the by now.
Our options in terms of science IMO are:
1) Wheel (7) - maths (14) - bronze working (8)
or we could go for bronze working first
2) Bronze (8) - wheel (7) - maths (14).
The second option is an additional 8 turns until we get siege catapult, but the advantage is that it allows us to know where iron is on the map a full 21 turns sooner.
We can then go for swordsman, especially if we have been lucky with second city placement and get some iron (/can ally with a city state such as Milan, which IIRC is a military cs and would gift us units).
For this reason I think I favour option 2, as my advice from role as sage and wiseman
Also, can I request that we purchase the hill tile northwest of our second city? This would block off the path through the mountain wall, and would hopefully secure our third city near Mt Kailash.
In terms of our war, capture and razing the first Siamese city, and then capture & puppeting of the capital would be my preferred strategy.