I like the idea behind it, I haven't played them lately however so I can't tell if it is working properly, I'll put it on my to-do-list.
So now I've tried the Ottomans out for a few games and while it is rather hard to analyse the impact of the UA, I'll give it my best choice.
The UA: The free caravansaries are actually awesome, I'm not quite sure if I think they're fun or if I think there could be a better solution, but they are good and they do help a lot(but probably less so than the other free building UAs).
The yields from finished trade-routes, I'm really not so sure about. The impact of that part of the UA is really hard to analyse as mentioned earlier. I thought the +200 Food/production from finishing a trade-route near the end of the medieval era was pretty good, until I inspected the incomes of the city sending the trade-routes (Istanbul) and realized that Istanbul was generating +200 food/turn (after bonuses and so on) and around 150 production/turn. I don't remember what my science per turn was at, but getting one turns worth of food and production felt kinda underwhelming.
I also lost over half my traderoutes before they could finish, by sanctions, war declarations and so on. I didn't get any of the wonders related to extra trade-routes but I'm not sure they would have made much of a difference.
All in all it is really hard to judge the Ottoman UA, under optimal circumstances it is probably really strong, but there are so many situations that are outside of your control that can mess you over.
The UB: The more I've gotten to use the Siege Foundry the less I like it, I was really psyched about it from the start. Faster cannons, stronger cannons, what's not to like? Well, the thing is that the gain from the Siege Foundry are actually pretty low (at least in my games), I tend to build A LOT of siege weapons assuming I have iron, but even with that, all you're getting is maybe a turn or two off every built unit and one free promotion. A promotion that you can get with a 30 experience investment. I mean I build the building in every city, naturally, the forge is nice and the siege Foundry is a forge but comparing the bonuses on the Siege Foundry with the two other unique buildings that buff produced units really leaves the Siege Foundry feeling weak.
Siege Foundry(compared to forge): +1 production +50% production while building siege-units, free early promotion to siege-units.
Ikanda(compared to Barracks): +unique promotion tree for melee/gunpowder units, +free unique promotion for melee/gunpowder units. (Now I'm kinda weirded out because the civpedia is really empty on this page, but I think it gives extra exp and extra crime-reduction as well, not sure)
Dojo(compared to armory): +5 experience, + unique promotion on melee/gunpowder units, +4 yields on horses/iron
Sure on paper the Siege Foundry looks somewhat equal (at least to the Ikanda) but free stuff for melee-units is going to be a lot more useful than free stuff for siege-units as siege-units both costs iron and are less likely to get killed (meaning you're less likely to build more of them). The fact that the promotions given by the other two buildings are unique also makes them a lot more powerful, sure volley is one of the best siege-weapon promotions, but it just requires one rank of accuracy to get.
The UU: The unique unit isn't bad by any means, but it is probably the weakest of all the musket-replacements, at least from my perspective.