From the save and in regard to your question:
Yes, you should take the 1500g that are offered to you in addition towards PP and Economics, because you already noticed that you will need to tech further and for that you need gold. 1500g + 2 techs are also enormously good trades and the chances that you'll attack Darius or Justinian are imo. not great, because Darius is supersmall but well developed (= you'll not gain much but that little will be hard to get) and Justinian is huge, I'm not sure you'd even have a chance against him at this point given your current strength.
I also don't think that you need to fear them trading MT to Alex or Peter (imo. the only logical war targets, Alex because he's big and underdeveloped and has the AP and Peter is big aswell, has the MoM and conquering him now could be the best chance you get, because Alex will still take quite some time 'til Rifles, Peter only needs PP + RP for them though, so enough for you to conquer him without fearing them but too little to expect that he won't have Rifles after your war against Alex) , if an AI has nothing to offer it's very unlikely that it'll get a tech, also: You have to thank the AI for every mounted unit that it builds, because those don't get defensive bonuses. A Longbow often is a harder enemy if he stands in a city than a Cuirr would be.
You'll btw. only get about 1000g if you trade PP and Economics in the right order from the right AIs ;D .
Regarding your build-up:
You can get 17 Cuirrs by upgrades (this will cost your complete gold + the gold that you trade for, but it's necessary and you also don't need to worry, because your empire is small, so you have a small deficit and you will be able to fuel that one by conquest gold.
Then whip away the Plains-Forest that your capital is working + the Plains-Cottage, your capital only needs to work the Grassland Villages + the food + the gems, this should be at least 2 Cuirrs with the Buro-bonus.
Edirne has almost no research potential, you can whip it down 'til it only works the food + maybe the Wine. All of the research-buildings in that city were superflous btw. and should have been units or Wealth / Research. From this city you'll get again 2 Cuirrs.
Ankara was a bad choice as a city, it has no own food and steals the food of the capital and it has only one decent tile (the Tundra-Horses) . Only found cities like that if you cannot get to 6 cities otherwise, this city is the reason why your capital is underdeveloped in size, it should be at least 15 at 1000AD imo. Whip this city down into the ground 'til it has nothing left except the food + the Horses, this will be at least 3 Cuirrs. (P.S.: Don't build Libraries in all cities, Ankara really has 0 commercial potential, don't think you need certain specific buildings in every city, evaluate city-builds in single. )
Bursa again has little research-potential with only 1 Village, but you're building a University. This is not as bad as it sounds, because you're PHI, but learn: If you want

, then build Cottages! Research doesn't come from buildings, it comes from land-improvements, buildings only multiply what your land offers. This city has no food btw. , don't found cities that have no food. It seems to me that you need to work on your early expansion, because it looks like you were completely boxed in and founded those cities because you couldn't get any others anymore. Doesn't matter, this city has 5 decent tiles (the Villages + the marble + grassland farm + the Ivory) so whip it to size 3, so it only works the Farm + the Villages to not lose your research. Not having the Marble + the Ivory for a moment isn't bad, because those tiles are about as efficient as the whip, so it's the right decision to grow onto those tiles in peace-times and then whip them away once you go to war. This city should be 2-3 Cuirrs.
Konya would have been a nice city to generate a GP, it has Fishes and no other good tiles and you're PHI. I wonder it has 0

, try to use the traits of your leader better and pay more attention to GPs and generate them in multiple cities, you don't need 1 GP-Farm for everything, you need as many GPs from all cities as make sense (and in the case of Konya, a GP would have made a lot more sense than working non-FIN-coast) . This city can be whipped down to size 1, this should be 3 Cuirrs.
In Samsun you're working 1

2

Workshops. Those tiles give you nothing, because 1

is about 2

(via the whip) so you basically pay maitnenance for the population that those tiles cost while they don't give you anything. Whip it down to size 1 (= 3 Cuirrs) . Next time you have such a beautiful Grassland city with a good source of

but little

, don't try to make a

city out of it, Workshop are goof from Chemistry onwards, not earlier. Konya could have been a really good 2nd

city even with not having a River or it could have been great as a GP-Farm because of all the farmable Grasslands.
Gazintep is the utmost crappiest city I've ever seen, it has no food and no good tiles. I have no idea why you wasted a Settler on that spot... doesn't matter, whip it down to size 1, it's gonna be 1 Cuirr. Learn now: Don't work Plains-Mines unless your city is size 10+. Plains-Mines cost you 2

, 2

are 5

when a city is small (again via the whip) so working a Plains-Mine actually costs you 1

.
Then you got 12 Forests, those are 12*30*1.25

= 4.5 Cuirrs.
Sum: 17 + 2 + 3 + 2 + 3 + 3 +3 + 1 + 4 = 38 Cuirrs.
A little more than the 20 that you mentioned

.
[EDIT]
And yes, ofc. , bribe Alex against Bismarck, wait 'til his Stack is in Bismarcks territorry and then backstab him. Try to at least get 4-5 cities simultaniously with those 38 Cuirrs. I'd probably not even capitulate him, because his land will make you strong, and capitulating him would damage your good relations towards the others because of combined diplomatic stance. It'll be easy to sweep over him with 38 Cuirrs and with 20+ cities afterwards you're in a winning position if you make it towards Rifles.