Emergence of The Ottomans
Conquering a city provides points towards a great general, and grants you a free Ghazi warrior. each city following your religion increases growth and great people genration in conquered cities by 5%.
I quite like the first part of the UA here, it works historically and would definitely incentivise big conquests. Though, like others have pointed out, it should be generalised to an era specific melee unit. The second half is a tad weird if I'm honest, both thematically and historically. Historically, most of the regions which Osman conquered around the Aegean and straight of Marmara would stay Orthodox for quite some time after his conquests and forced conversion isn't really documented in his reign. So if the angle here is 'conquer and convert for bonuses' it doesn't work historically. Equally, if the angle is 'Go wide and religious for max buffs' that also doesn't work, given Osmans little khanate was barely the size of London. The first bit works because it doesn't require you to have a big empire to be a strong warmonger - just like Osman, however the second bit doesn't. Furthermore, additional GP generation and growth is an odd bonus for an obviously war-focussed civ. Surely it should be something like gold, experience or production?
Ghazi Warrior
replaces Longswordsman. has lower strength(18 ). has a bonus against cities(33%). per each city following your religion, the Ghazi heals 1 HP per turn (up to 10 HP),and gets 2 faith from pillaging tiles(up to 20).
I love this, though I think its overpowered. I'd get rid of either the bonus against cities or the additional healing. That said its still very nice.
Timariot
replaces knight. the Timariot is weaker then the knight(18 ), but starts with the Shock I promotion. it has a bonus in friendly territory(25%), and is cheaper then the knight. upgrades to the lancer.
Cheaper but weaker is a really odd bonus for a unit which is supposed to represent the political elite of the Ottoman Khanate. Furthermore, the bonus in friendly territory makes no sense given the overall theme of the civ so far has been offensive war.
UA: The Conqueror
Each ranged unit adjacent to a city reduces its yields and its defensive strength by 5%(and siege units by 10%). ranaged Ranged units have a 33% bonus against naval units. after reaserching researching the required technologies, receive gunpowder for free.
This UA is a tad cluttered, though of course thats just my personal vendetta against 3 sentence UAs coming through again. I love the first part - really works in representing Mehmet as a master of siege. If anything I think the bonus could be upped a little bit. Its fairly rare to have siege units adjacent to a city anyway, if it can be helped, so an extra boost wouldn't go amiss. I'm not sure how useful the second bit would be, nor do I think its very thematic given it cuts out the navy, which was historically pretty strong in the Ottoman Empire. Furthermore, though the gunpowder thing might make sense gameplay wise - historically the Ottomans didn't adopt gunpowder any sooner than the Europeans, they just used it a lot better. A bonus to siege units would make more sense than early access.
UU: Great Bombard
replaces cannon. unlike the cannon which it replaces, the great bombard has a smaller bonus vs. cities(150%), and does not need to set up to fire (but may only fire if it hadn't moved in the same turn). has 28 ranged strength, and 11 defensive strength.
Must be harsh here; I don't like this at all. It just doesn't make sense to me - the Great Bombard was famous for being this enormous unwieldy behemoth that took dozens of people to move and could only fire a few times a day lest it overheat, but packed a hell of a punch. So the bonuses you've selected make it weaker against cities, stronger against infantry (These cannons were never used against infantry) and faster? Weird. Furthermore, the extra movement point thing means nothing in real terms, as has been pointed out.
UU: Humbaracı
Replaces crossbowman. unlocked at gunpowder, and has a higher production cost. may only attack adjacent units. however, the Humbaraci is stronger then the crossbowman(15 , 22 ). it also boosts the strength of adjacent gunpowder units by 15%, and has the volley promotion.
I like the idea here, but honestly I can't shake the feeling that this is a huge step down from regular crossbowmen. The reason people spam crossbowmen in civ is because they are ranged, therefore infinitely better, so it seems odd to get rid of this bonus. Other than that I like it.
UA: Community of the Talented
engineer and scientist specialists increase culture and faith by 5%. after the respective guilds have been built, the palace will contain cultural specialist slots. world wonders provide double GP points.
I like it, though I'm not sure how well the flat percentage increase will work, could be overpowered if you snag enough specialist buildings or wonders. A yield from specialists like say +2 faith and +2 culture might be easier. I love the palace thing - really captures the intricacy of the Ottoman court. I don't like the third bit just because it clutters up the UA and seems odd given how few of the actual ingame wonders Suleiman built. (Count: 0)
UB: Medrese
replaces university. Has one extra scientist specialist slots, and increases the yields of all science buildings and specialists by 1 faith.
Love this.
UU: Barbary Corsair
replaces privateer. has a combat bonus in coastal areas(20%), and starts with the Boarding Party I promotion.
I like it, but I'd rather it just get the 'capturing ships' thing from the vanilla UA. Personally I feel that splits should try to take as much from the original civ as possible.
Further thoughts:
Ottomans without Janissaries is just odd - should really be worked into one of them.
No civ with anything about religious tolerance is very strange - its one of the most important parts of Ottoman history if you ask me. (But then I'd say so, having written like 12,000 words on the subject a month or so ago!)
Hope this is more what you were looking for bro!