OK, let's sum this up, at the total cost of education and about 1000 gold we got
Gunpowder
Drama
Music
Philosophy
Guilds
Nationalsim.
I say that getting Fuedalism/theology/Gunpowder/drama/music/philosphy/guilds/nationalism is a fair price for losing teh liberalism race. The only problem is I tried my best to get astronomy to no avail.
I agree, this was pretty decent. Losing the Lib race lost you one free tech, and while this hurts it's not a game-breaker. Getting to Lib first is a bonus, as is getting the Oracle first or stealing a Worker early. None of the above are needed for a win, let's keep that in mind. You've traded Lib and Education for some expensive techs, including Nationalism, which is great.
We start getting a little more bold and form an assault force to take a barb city.
This coastal barb city is going to be an excellent production center later on (I've built Heroic Epic, Military Academy and Moai Statues there in my game).
What I do not understand is WHY there is some unhappiness from we wish to join our old home??
The Barbarian State does build culture as any other civ, only a lot slower. If you wait long enough you see border expansions on Barbarian cities.
After liberalism, I swap civics
FR may be an issue in diplomacy and I may have to revert to Buddhism/theology to make friends with Justinian and Saladin.
Frankly, I have no idea why you did that... big mistake. What is FR good for in this situation? What you want now is Pacifism, or Organized Religion maybe, but not Free Religion.
Go research Constitution next so you can run Representation, and then switch to Pacifism and Caste System. If you do some quick math: 7-8 specialists are easily supported in Lisbon; each of them will get a +3 beaker bonus from Representation, so that's 20+ additional beakers after Representation from the former capital alone, not even counting all the other cities where you can convert weak/unimproved tiles into a 6 beaker scientist.
Yes we are still in a hole. I say we need to target the internet somehow.
You're doing fine. I don't quite recall the details, but I was probably in a similar tech situation at this point in the game in my second attempt, and later on I couldn't trade techs anymore because I was ahead of everybody. I did end up building the Internet, and got zero techs out of it (but kept it out of the hands of the AI).
The AIs will continue to spend resources on wars, and as long as you don't get dragged into one they won't be able to beat you in the long run, with all the precious land you are about to settle.
OK, I think I am planning on taking out those remaining barb cities filling in with other cities, and build a new FP in the north once we spin off the Old world.
Something to keep in mind, because it's somewhat easily forgotten: Communism. With State Property you don't need any FP/Versailles anymore, and can start plunking down cities almost at will.
In my second game I ended up not building the FP at all. I was thinking about rushing Versailles with a GE at one point, but when I got beaten to it I was almost glad. I simply researched Communism after Scientific Method, switched to State Property and stayed there until the very end of the game. I couldn't build those settlers fast enough anymore. All of the coastal cities would pay for themselves right off the bat, due to the trade routes. Founded an almost useless city on top of ice marble, just to get the resource -- the city even ran a profit

.
So Astronomy, Constitution and Communism are the key techs in this phase of the game. Astro for commerce, Constitution for research and Communism to allow for a land rush (the AI won't hold back on those new lands forever).
Those Old world cities are depressingly supporting the entire economy.
That shouldn't be depressing as it is normal at this point. BTW you can't liberate these a lot earlier than 1776 AD. I couldn't have afforded it in my game and still win, and you won't either -- that's pretty much guaranteed. So don't even think about pulling that "liberation trigger" any time soon.
OK, so I say we tech off astronomy and see what we have. AFter that I think we really need constitution/democracy as we are having some emancipation declarations plus I think we want to quicken cottage growth pace.
It's a shame that you have to waste so many turns researching Astronomy now. How unfortunate it was to get Horseback Riding instead of Astronomy from that goody hut

. Anyway, I agree with Balbanes that there's probably no way around it, you need to get it soon to connect the two continents and boost your income.
BTW as soon as Astronomy connects that Marble to Lisbon you should build the National Epic there, if not earlier. And also build the Heroic Epic in the best of the "old" production cities, and don't forget the Moai Statues.
All of the National Wonders you can build again at a later time in the new world.
Tech order should be:
Astronomy, Constitution, Scientific Method, Communism (for the reasons mentioned above).
Trade Nationalism to as many civs as possible, so they can research Constitution for you (trade for Astronomy then).
OK, the truth how bad am I doing.
Not bad at all. That civic switch was boneheaded, sorry I have to say that, but apart from that it's not as bad as it seemingly looks to you at the moment.
At some point in the game you will start recovering really quickly and probably take the tech lead at some point.
The biggest danger still are wars getting into your way, or the diplo situation getting out of hand, not the economy, which will recover.
REPRESENTATION, CASTE SYSTEM, PACIFISM!
Do it. Astronomy will improve your situation drastically.
I agree. Since I always got it so early from the villagers in my own games, I don't even know how it is to delay Astronomy here, but it can't be a winning strategy ;-).
The 10% research is not worth it to have the majority of the world drop down from friendly and pleased to cautious or annoyed.
Not even speaking of the loss of the 25% production bonus for buildings... which is what pretty much every city in the new world is making right now.
Space Race might be possible if you beeline the internet.
Space Race is possible simply by staying out of wars (unless you have a runaway AI that totally gets out of hand, but they'll end up declaring on you at some point anyway).
We're one third into the game right now, I don't understand why everybody is so panicky...