Gee, can I finally post this now??
Day before yesterday was the climax for my course with the exam being held, so yesterday I was completely wasted. I woke up with a headache, sore and tense all over, and things didn't really improve

. But the good thing is, the course is (more or less) over, which means more time for civving!
I've tried to reconstruct what I wrote that was eaten, but some of it has been said already.
Military
Carthage
The stack moving on Carthage should be enough to capture. Since Hannibal has been using his Numids in offense, I doubt there will be that many left as guards in Carthage, I would guess 3. With the troops we have, assuming no counters, that's well over 95% chance of capture. If we get a counter, or if there are 4 Numids, the odds drop to about 91%.
Move the sword on the cat stack one step along the road towards Carthage on turn 0, hills is better bonus to defense than fortification, and there's no way Hannibal could send a unit around that position to strike at the cats.
When you attack, a general rule of thumb when using mixed forces:
If the question is whether to succeed in capturing or not, always use the strong but slow units you have first, since they has the greatest chance of taking out the strongest defenders right away.
If you are certain to win, and need the forces for further action, start with the fast attackers since they can retreat, which means average losses will be less.
Carthage clearly falls under the first category, so use the swords first.
Edrine
Some units could reach Edrine a turn faster, but they wouldn't be enough to capture with fair odds. Wait until all the units get there, then attack. Bring in the sword that has been healing in Karakorum, and you should have enough units fully healed afterwards to press on to Istanbul.
Infrastructure
I set lots of towns to building libraries, we want the expanding borders fast not to mention the effect of the libraries themselves. I think we should rush the lib in City for the Sages as fast as we can, when the border expands there we'll get access to the oysters which are not only super-commerce tiles, but also food bonuses for faster growth. And it also means that we can start the Copernicus prebuild faster (after market).
Some towns that have very high growth potential (Zentral, Cabana, Missi?) might be better off with a market first, with the silks from Carthage that means we can get up to size 11 with lux rate 0%, instead of 7 without it. Would anyone care to do some calculations on this? I could do it, if only I get the time before WD plays.
In general, build sequence in all these towns should be something like library - market - (harbor where needed) - courthouse (except in Zentral) - cathedral/uni.
I've followed CF's good example and named some settlers, but of course you may choose to place them somewhere else.

And yes, the three towns disrupting RCP should go away fast.
@CF: Are you sure that's what happens when building a settler at 1 pop? I was under the assumption that even if you have only 1 pop, if you run at 0fpt you are asked if you want to disband. I would have thought I would have noticed if this wasn't the case, I've relocated quite a few towns in my days, but when I think back maybe all of them were pop 2?
Research and Trades
In 4 turns we can start researching again. And our potential is really massive, at the current count (which will increase) we can do Monotheism at 100% research in 5 turns at -84gpt, or at 0gpt in 9 turns.
We have lots of money. Really lots of money. But still we could only keep up 100% research for about 13 turns before we have no money at all. But what else to do with the money? We could rush libraries, courthouses and markets, but they will never be able to repay themselves. Only if we are already running at 100% research will rushing such buildings make sense. No, I say full speed ahead towards Education (once Otto's are down), with few exceptions (like the library in CftS).
We should be able to get Currency in a peace deal 4 turns from now, and thus be able to start research on Monotheism right away. It is possible, but unlikely, that we could get peace with the Ottos in the same time. But since we're not yet at 4-turn research, the speed of our research will be measured in gp still. So running a few turns at 0% research, just hoarding money, will not slow us down the least, it will only prolong the time for which we can run at a deficit once we start.
My suggestion is thus to get Currency fast, take reasonable time (6-7 turns?) to deal with the Ottomans while running at 100% tax rate, gift up the Ottos, and then start research at 100%.