Right Darzee, you're about to get one of my longeer posts
I've had a look at your save, and you aren't doing nearly as badly as you described. You are the largest Civ (by land
area), you have the largest population in the world, best income, productivity, culture etc. You also are the most advanced Civ technologically.
If you want to go for a builder-type victory, there's not much you should change
However, there are quite alot of things as a rule of thumb that I would
not do, which you currently are.
The most prominent one, is leaving your Border cities completely undefended. I can only see 2 which are, and they only have a warrior in each. If you want to progess up the levels, this is one thing you will want to change. I'm surprised the AI hasn't attacked you yet (Unless that ruin next to Adyin was yours?) On the higher levels, the AI has a strong tendancy to sneak attack you, alot of the time without any logical reason. But leaving your cities like they are would give them a reason.
If in a republic (like you are), you have gathered the right principal of not having too many units. Although you seem to have taken this to another level
You don't have to defend your inner cities, but the ones which are bordering with other Civilisations definately need to be defended by at least one
good defensive unit -- maybe 2 or even 3, if that city is in danger of culturally flipping or being attacked. Then again, if the city is in danger of flipping you should really have more than 3 units inside it...
At this late stage in the game, your chances of winning a victory by culture are limited. Even though you are the cultural super-power, you will have no where near enough to get a victory before 2050 AD. Hence, I see no point in you building all the wonders. They may seem nice, but they aren't worth it in comparison to how you could use those shields otherwise -- if not building the wonders. You could build yourself an army instead, and conquer the world!
Regarding choices of improvements that you have built. The most noticeable mistake, is that you have a barracks in every city. Ok, this might be acceptable if you were a warmongerer, and building an army, but... well... you aren't. This is immediately 10gpt down the drain, every turn, for a feature that you don't use.
You placement of courthouses also seems quite odd. Unless you have corruption in your cities, there is no point trying to lower it. I went around selling all of the courthouses in your cities, and there was almost no corruption in all of them. So another note, don't build courthouses unless you really need them
You again could have spent this time building an army or whatever.
As for the rest of your infrastructure, it looks quite good for a builder type game. Although there really is no point building wealth. Stop it!
Note: Some of my advice so far has kinda been geared towards a warmongering type game, this is not intentional. But it is the quickest, and highest scoring way to win. If you were to be a warmongerer btw, it would be more suitable to be in a Monarchy (but I think you know that anyways)
Moving onto trade. You can't trade with anyone! You should really establish a road-route to your neighbours, and exchange resources with them. This way your people will be kept happy, and you won't even need to build colluseums etc. You could then spend that time building an army. It also improves their attitude towards you, so you are more likely to win a diplomatic victory then.
My 2nd last point, you should aim to expand more vigirously. It took you Just over 4000 years to get a fairly small empire -- although it is large in comparison to the AI's. You should read some of the articles in the war academy to help you with early expansion, as you will notice the AI improve alot in this section as you go furthur up in difficulty. You would also benefit from building your cities closer together (if going for a war-type victory)
Last, but not least, you are easily the most powerful nation. All of the Civs around you are weaklings. If you turned your eye towards building an army (in all cities) for ~20 turns or so, you could probably conquer the world! Take heed
There's something else that I can't think of right now, but I hope all that helps
Take it as constructive critiscism.
Edit: Ahh, workers! 7 is simply not enough. For an empire that size, being industrious, you probably want ~15, and when you have improved everything, you can simply build them into your cities (or wait for RailRoads to come along)
Another thing, that map looks a bit nasty with all the mountains, and its kinda annoying how you cant go around the world horizontally if you know what I mean. This would hinder your progress in a Conquest/Domination win. You should allow X-Wrapping.
For anyone else reading, the game is C3C, not sure what version, but it works with 1.12b