Finally I played my turns. That's not so catastrophic, IMO. Some good things happened, some bad too, but this game is definitely winnable. We just need to be GOOD and LUCKY, as Sirian said.
1950 (inherited turn): I see that our cities are only building military, then I watch the civic screen, and revolt. I'm a CivicFanatic, you know...
Going to Theocracy from OR, so we have 1 more promotions on all this stuff, and save a little money. OR wasn't useful at all.
1951: Attacking sparta. Railroads allow direct attacks from our mainland, I place a MG on a hill and start sending in units, outdated too, we need to get rid of all tis junk which is costing us money.
Tank defeats (15.40/28): Mongolian SAM Infantry
Infantry defeats (12.40/20): Mongolian SAM Infantry
Infantry loses to: Mongolian Artillery (5.58/18)
Infantry defeats (9.80/20): Mongolian Cavalry
I'm amassing troops at samarqand, too. Lots of nasty cavalry, they kill some units. The difficult part is establishing a solid base near the city: once you have 1-2 MGs you can start adding units. If you don't have cover the cavalry will hurt. I left some units alone (not too many...), and they were wiped out easily.
Machine Gun defeats (14.94/18): Mongolian Artillery
Machine Gun defeats (6.48/18): Mongolian Cavalry
Tank defeats (19.60/28): Mongolian Cavalry
Tank defeats (3.92/28): Mongolian Cavalry
Machine Gun loses to: Mongolian Cavalry (15.00/15)
Tank loses to: Mongolian Infantry (20.00/20)
Machine Gun defeats (7.38/18): Mongolian Infantry
1952: Spy production is started in pharsalos. ASAP, you said? No problem.
Training pays off... close call, I'm glad I promoted the unit first.
Infantry promoted: Combat I
Infantry promoted: Combat II
Infantry defeats (4.00/20): Mongolian Cavalry
Now... the Battle for Sparta:
Infantry defeats (9.80/20): Mongolian Artillery
Grenadier loses to: Mongolian Artillery (8.82/18)
Tank defeats (28.00/28): Mongolian Artillery
Tank defeats (26.60/28): Mongolian Artillery
Easy... the cavalry mysteriously vanished. Only artillery was left in the city. And Destroyers...
Infantry defeats (11.60/20): Mongolian Artillery
Captured Sparta (Kublai Khan)
Ewww! Sparta is full of Germs! We need to rebuild our protections!
Sparta begins: Granary
Some effort to kill an infantry in the woods:
Infantry loses to: Mongolian Infantry (13.60/20)
Rifleman loses to: Mongolian Infantry (8.40/20)
Rifleman loses to: Mongolian Infantry (0.60/20)
Rifleman defeats (14.00/14): Mongolian Infantry
I know, I should have saved the infantry...
1953: Nothing big, preparing for the Cold War (aka spy completed, start another).
Killing some stuff in Samarqand, too.
1954: Hello Cathy. What do you want from us?
Of course, we'll do whatever you... wait... war? Rotten bodies attract Germs! We don't want war! Go away! Go away! Only mongolian bodies don't attract Germs

.
Then, killing stuff as usual. Nothing big.
1955: Hello my friend Franklin Delano. What? War? With Russia??? Russian Germs! Ewwww!
Of course I decline both requests.
Training for the Cold War. Sci to 60%, we're losing much money.
1956: The Battle for Samarqand!
Tank defeats (21.28/28): Mongolian Infantry
Tank defeats (5.60/28): Mongolian Artillery
Tank defeats (15.40/28): Mongolian Artillery
Rifleman loses to: Mongolian Artillery (4.32/18)
Infantry defeats (20.00/20): Mongolian Artillery
Captured Samarqand (Kublai Khan)
The city is ours! Should I stop? Why? I've got so much military! FORWARD!
So many Germs...
Samarqand begins: Harbor
In the interturn, we learn that once Boston used to exist... razed by Cathy. FDR is totally crippled.
1957: Cold War Training.
1958: The enemy tries to stop our advance at Old Sarai:
Tank defeats (24.08/28): Mongolian Artillery
Machine Gun defeats (13.50/18): Mongolian SAM Infantry
Yawn.
1959: You know, I like war. The Battle for Old Sarai!
Tank defeats (28.00/28): Mongolian Artillery
Tank defeats (20.72/28): Mongolian Artillery
Tank defeats (22.12/28): Mongolian Artillery
Captured Old Sarai (Kublai Khan)
Stop? Why?
1960: last turn, I know you are all thanking God I've finished my turns... I have pushed the war a bit over the limit suggested by ChrTh. Well, maybe two bits
The Battle for Beshbalik!
Artillery loses to: Mongolian Infantry (8.00/20)
Tank loses to: Mongolian SAM Infantry (2.34/18)
Tank defeats (9.52/28): Mongolian Infantry
Tank defeats (28.00/28): Mongolian Artillery
Tank defeats (28.00/28): Mongolian Artillery
Artillery defeats (18.00/18): Mongolian SAM Infantry
Captured Beshbalik (Kublai Khan)
Easy... I've established a secure line of protection for artillery, which could bomb beshbalik's defence from 80% to 0% in two turns.
We have the power to wipe kublai khan out.
We're a bit behind Liz, however... This is still winnable.
First, we should go for kublai, the more land we have, the better. It's additional beakers! Why not, we've got the opportunity to do this. Kublai could give us rocketry and maybe some cities for peace. I'd take New Sarai and Karakorum, then grabbing rocketry for peace.
I couldn't raze samarqand and sparta, for some reason. I didn't get the opportunity. So I decided to take some more land...
There's a small window for us, still, but it's very small. Liz has built the 5 casings, the 3 thrusters, and the docking bay. This means she has robotics, so she's building the space elevator. If she gets it, it's over. No way out. We must build it, we're only one tech away from it, and we should rush-buy it. It's doable, even at the cost of losing population lowering the lux slider we must take the risk.
A war with liz seems almost mandatory, even if she has more power than us. The 4 spies are on a transport, and we must find out where are her forces, and maybe build some nukes. We must use all we have, nukes could be critical.
The spies could disconnect liz's aluminium... Sabotage... destroy oil wells and farms... we must cripple liz the most possible. Take out the improvements! The happiness isn't a problem for her, with all modern wonders. Go for the health!
The strategic disadvantage she has is being on the sea: we could potentially find the apollo city, nuke it 2-3 times, land some marine tanks and raze it in 1 turn! We should take the choice.
Our strategic disadvantage is that our best production sea cities are on the other side of the landmass, so our navy will be somewhat weak if we attack. A blitzkrieg could be the best option.
Tech-wise, I think the fiber optics choice was sub-optimal, since we won't have much room to build the internet (unrushable), and its use will be limited. Tech suggestion: robotics ASAP (even 0% lux). Then maybe fusion?
Beware of Cathy, we may declare to america to increase relationships, she's annoyed and could smash us anytime. Try to appease her!
- Oh, and welcome to the Sixties

!
mucco
EDIT: the save...