So, it took me four tries but I got my first win on Immortal with 9 total Civs. In two of the first three games that I didn't win I had stone nearby (once right in Moscow) and built the Pyramids (I don't think I ever built them on any of my previous games working up to Immortal). In one of the games, I was able to build maybe five wonders with the help of the GEs that I got. I was going to go for a Space Race win but even with some pretty good games I eventually fell behind in tech. One game was looking halfway decent until I discovered Saladin as the 9th Civ relatively late in the game, only to find him to be more advanced than everyone else. Another game Mansa Musa built the spaceship. One of the games I switched and attempted a cultural win but just couldn't get there.
I looked for opportunities to attack but just never felt strong enough at any point to do much. Any effort made in that direction would just lead to me underdeveloping everything else and by the time I get Cossacks most of the others usually have reasonably comparable units.
So, in game 4 I went in with the plan to try for a Cultural win from day 1. The random map turned out to be Panagea and I met all the other Civs relatively early with Hatshepsut, Tokagawa and Napolean bordering me. I wasn't that thrilled with the last two being there and Napolean barely beat me to a good spot for my fourth city and I still decided to settle only three squares away because there were like 5 Dyes and a Banana possibly available. I was able to avoid war with the latter two the whole game, even though Napolean got annoyed with me a number of times. I ended up building two wonders, the Sistine Chapel and the Taj Mahal.
I got two religions relatively early on but really never got another one and was still able to win despite having only six cities as well. I was trying to get Buddhism for my third (a cultural flip would have put that in my wheelhouse) but a size 1 city that was completely surrounded by my land held out forever and by the time it flipped it was too late in the game to make a difference. That was actually Napolean's city where he tried to get all the Dyes at the beginning.
I've read about people trying to get to Liberalism first and I tried that for the first time. I was generally one tech ahead the whole time, was researching Education with no one else having it and just as I finished it, Asoka somehow finished that and Liberalism on the same turn out of nowhere.
Moscow and Rostov (the Dye city) each had close to 400 culture per turn once I got everything fully into culture mode. And then I had Novograd with about 200 per turn. I even had St. Petersburg that I could have chosen as one of my three cities as well. I got the Great Artists all the way up to 2200 by game's end.
There was some danger when I entered into a Defensive Pact when Tokagawa asked me. I did it and then immediately on the next turn Hatshepsut attacked and I was sucked into a war in 1804 with the points leader in the game. At game's end, she ended up having 2900 and I was last with 1500 (but normalized I got almost 15000 when I ended up winning in 1858).
She had Tanks, Artillery, Marines and Infantry. I had Grenadiers and a few Cossacks plus some lower level units. Fortunately my cultural boundaries had expanded things to the point she had a lot of open ground to cover to get to my cities (excepting my only coastal city, which she got to and razed right away). Plus I had nothing to do with my workers for awhile so just to be doing something I improved all the tiles in the middle of nowhere and she spend time destroying those useless improvement as well.
In the end, I was able to hold her off - I had the fallback plan of giving her St. Petersburg (that she kept asking for) but things never got quite that dire.
Asoka got to The Apollo Program in 1650 and quickly built the initial parts of the spaceship but somehow no one got beyond building the thrusters and I didn't have to worry too much about that.
That was a fun game! But I could never really relax at all. Now I will try with 10 total Civs and see how I do. Each additional Civ will make things that much harder.
So much better than playing Deity which doesn't even feel like a real game with the excess advantages the AI gets.