3. Techs, I'd say Wheel-> sailing-> masonry -> HBR(?) chances to me seem quite good that Lizzy has no copper, which would make a horsearcher rush seem like a walk in the park. I'm normally not playing on immortal so I don't know how fast everything is enveloping,
I wouldn't rely on Liz having no Copper - we can't see many of her tiles, and I've seen plenty of Immortal AI starting with Copper in their capital's radius. Still, she doesn't appear to have Bronze Working... yet.
I don't think I agree with going for HBR... I think it'd be preferable to check if we've got any Iron first. Besides, I've always had reservations about HBR since it's a dead-end tech. (Although I guess it still has trade value.)
There is one perfect place to block Liz off in the west, on the river directly east of her horses. Being creative, your borders will pop leaving her with very little land (and no horses assuming there are none to her west), and completely cut off. If this is done Liz can sit idle there a long time before she tried to expand and will be content with a few cities, all the time letting her build an impressive city structure for you to claim post-construction (as well as perhaps the Hindu shrine).
That's a very valid point. Of course, it all depends on where Liz is settling... it'll still be a few turns before we can get a Settler in the area, and she may have blocked us off already by then.
Alternatively you can put everything into chariots and rush the blazes out of her, my guess is she may NOT have BW yet and not be able to whip defender. Also if she has a second city founded she has committed hammers to a settler, increasing the chances of a very successful rush. We also know that there are no leaders to the west due to the eps.
She certainly doesn't have BW yet, although I suspect she might not be far off. Once she can pop-rush Archers, things become a lot harder... and if she has access to Copper, we can forget about it.
Amsterdam: Second worker, a warrior or 2, then a settler. A rush would work but she's kinda far. We don't know if she has copper in her BFC.
She's as close as we're likely to get on this kind of map. Plus, if we found a second city near to her, she'll seem much closer. I don't think distance is a good argument against rushing, because she's really rather close. (And of course, we'll have Sailing soon, which will mean we can connect up any of her cities that we take fairly quickly.)
Techs: The Wheel, Either sailing or pottery/writing. Sailing for the 3-insta commerce coast tiles pottery for financial cottages or writing for creative libraries. GLH I'd avoid because it's too powerful on this kind of script imho.
Avoiding the GLH because it's too powerful? Sorry, but I've already said that my aim isn't to play a variant where I deliberately ignore a certain strategy because it's very good. The only reason I'd pass on the GLH would be if another strategy - ie rushing Liz - looked like it would yield a greater net return.
Pottery/Writing are certainly techs that we want to think about in the not-too-distant future though. Depending on where the AI are at that point, I'd consider going for Alphabet too, since we already know 3 rivals and trading could be valuable.
Depends on plans if you plan whip or grow capital to size five next warrior will sit for happiness. Will you build second is matter of long term plans... Probably scouting closer area is better.
I don't think I'd want to whip this capital below size 4, just because of the fact that it has 4 particularly powerful tiles to work at the moment. But certainly growing to size 5 would be reasonable, and whipping from size 6 to 4 could work too.
I would plan second worker as soon as cap grows to size four. It will happen same times as warrior is finished if you switch one of cows to fish.
Problem is another Worker delays a Settler, and we probably need to get out a Settler ASAP if we want to have any chance of blocking Liz off.
most likely wheel... Although if you plan to settle that gem spot soonish it might be case of IW. double riverside gems while financial is so sweet...
Very true - if we can manage to settle the Gems spot (which by the way I'm dubious about), then that gives an extra incentive to get IW as soon as possible.
Presumably there is quite a bit of territory to the east, as we have met two civs from that direction, so it might be worth getting at least one more scout (not an actual Scout of course) out in that direction soon so we get a better lay of the land, find where the other AIs are (if they are close - they arrived at 20 and 22 turns, so they could be fairly far off, especially if it was Scouts, couldn't see), depending on how direct a route they took. A second warrior to defend the city and avoid the Republican voters in the city being unhappy would also make sense.
I tend to agree with 3 Warriors: one to defend the capital, one to explore west, and one to keep track on Liz to the east (as well as guarding the Settler if we send it that way).
As for the worker I would normally prefer to chop the hills first, so that when the worker has time he can put mines on them, as that increases our tile working options to switch to a higher production mix when we don't want as much food (i.e. in between whips). That is some turns away from chopping though, and with 4 good tiles and population capped at 5 (and probably 4 effectively while whip unhappiness is running) until HR/trading/new resources, maybe +1H +1C that we might not always be using isn't worth it. Still, we are likely to want to switch away from food a fair bit of the time, so at least chopping the plains/hill/river seems like it is worth the loss of 1 worker turn.
Only issue with the Worker going to the hill is that it'll delay hooking up the Horses, because as you note yourself, it'll take a while to chop + mine on Epic.
for the 5th question, let the worker build a mine on the tile SW of it, this will get the city to grow right after the 2nd warrior, and then gets the chop in the Settler-build.
The mine is done one turn after the wheel is done, so then the worker can road to the horses and pasture them.
Have you tested this? If it'll be only a turn or two of delay in hooking up the Horses after the chop + mine, maybe it'd be worth getting that mine in place. It'd certainly be useful as soon as we get to size 5. (Then again, size 5 is still a little while away if we're going to build a Settler or Worker at size 4.)
You don't need to have it one way (GLH, leave Liz alon e for now) or the other (chariot rush) - a chariot pin will let you have your cake and eat it too. 
BUG)
However, there are certain physical limitations in the game, the main one being you can't build two things at once. Even I can't build a dozen Chariots while managing a Lighthouse and Great Lighthouse simultaneously. 
