I took a look at your save. Here is my advice:
#1-Build terrain improvements. Very important. You only have a few squares covered with roads in the cities' boundaries. There is no reason to be falling behind in tech other than low revenue due to unimproved terrain. Look in your city panel and see what terrain is being worked. Build roads and other improvements in those squares.
-Grasslands should be mined.
-Hills and mountains should be mined as well.
-Plains should be irrigated.
-Forests that are not being used should be cut down, you get 10 sheilds and there could be a bonus grassland underneath.
-Everything else being equal, terrain next to rivers are preferable to those not. The reason is that all terrain adjacent to a river gets 1 extra commerce.
-Build roads in all wroked squares, they will all provide extra commerce.
I see that you are irrigating the grasslands around your capital. As ia have mentioned, there is no reason to do this. Simply mine them and you will automatically get 2 food from each terrain, which will support another citizen to work the next tile. Irrigating grassland is useless before hospitals and I don't do it after, unless it is in a city surrounded by mostly desert.
In order to improve terrain you must build workers! You are playing what appears to be a huge map, and you have 5 workers and a handful of slaves (captured enemy workers). Keep in mind that slaves work at half the effeiciency of normal workers, lazy maggots. Always have 15-20 workers by the beginning of the Medieval age on a huge map.
#2-Upgrade your units, and on border cities have at least 2 up to date defensive units and at least 1 offensive unit. In the interior you can get away with offensive units. They will count more toward your military's reputation anyway. There is no reason to pay a gold per turn for a warrior when you can pay the same for a knight. You are coming to the end of the Medieval period, and you have mostly spearman and archers. These units are far past obsolete and will not help you against modern units.
#3-Do not build wealth before you have the Economics tech. It is a waste. Simply keep building workers (with your smaller cities) and military units with your larger. If nothing else is happening, plan an invasion. I see that in Kyoto you are building wealth, when it could very well benefit from a bank, well it could if it had more roads.
As far as war with the Ottomans, it could go either way. Their invasion force wouldn't be considered threatening if you had better garrisoned your outer cities, and had better production with which to build units. You may lose some.
What you may try is puling out of your farther cities, and putting a big garrison in a closer city by making a stand and bottlenecking you terrain at the same time. This will force them to engage that city or leave them open for attack when passing by.
Or, you could switch all of your cities to building military units and hope the Ottomans are incompetent enough to fail taking even one city. I doubt this though.
One final option, and this is what I would do:
You can quit this game, start over taking the advice I've given you about improving terrain and keeping the army modern. But before you start another game, read the articles of the links below and pay attention because they will improve your technique. Then, start a new game with a civilization that you would excell with, but this time play on Warlord. Go straight for it. It's easier than you think. You won't learn much on Chieften because the oppenents are handicapped and they pull their punches. Seriously read these key articles. If you feel like reading more, do that. And remember, build workers and improve terrain!
Good luck.
Babylon's Deity Settlers
Cracker's "Improving your Opening Plays"
Faster Expansion
Commercial Management
As far as military advice. Simply read the articles that focus on the area with which you have trouble. I haven't read any of those. Perhaps I should. But anyway, move up in difficulty, you will learn more from losing than winning, provided that you don't give up at the first moment it looks hopeless.