Lets say I made the culture wonder for the Japanese. And then my culture spreads to another players nation. Can they now build their own Samurai too?
It would depend on how strong the Japanese culture is in a city. The Samurai could require, say, 25% strength of the culture 'idea' in a city for that city to qualify to train them. Even in your own cities, not all of them may have strong enough Japanese culture to train the Samurai. However, you could use Japanese cultural buildings and/or Storytellers trained in cities that have primarily Japanese culture, or those who have promoted to 'learn' how to spread Japanese culture, to boost the strength of Japanese culture in your cities so that it starts to get ahead where you want it to so that you can start to be able to build Samurai where you want to.
If you spread out your Japanese culture to other nations with said storytellers or by creating immigrants from primarily Japanese cities and sending them to join other cities in other nations, you could start to push your Japanese culture outward, which could give you a strong capability of eventually fracturing your opponent's nation, without war, and having some of your opponent's cities potentially even join you when you later decide to (with civics) adopt the Japanese culture as your national identity.
But in the meantime, yes, it would mean your opponent could also potentially build his own Samurai in those cities that you've been pushing the Japanese culture.
One of the main things we're hung up on at the moment is trying to determine a set of rules that guide the growth of and shrinking of cultural values, what mathematics define their spread, waxing and waning. I'll have to start giving this deeper consideration and expressing some ideas here for that.
In essence, each 'idea' would be like its own property and it would be nice to use the property system but I think that system may be too much for it in processing time and the trade aspect of the property system isn't working properly anyhow. I think it can be done a little simpler in the code.
Will hero units now be like world wonders where players have to rush to build them before another player gets it?
You'd probably want to have to have a fairly strong influence % prerequisite for a culture in a city to train a hero, like 50% or so, which would be easiest for the city that has the initiating wonder for a culture (which would initially be the core source of modifier to increase the influence of that culture in the world, starting primarily with the city it's in) but yeah, there could be a race for them and many cultures may never ben promoted enough in a nation to get the hero out of it anywhere in a game, which is what will limit their impact on games, which is currently said to be too strong because you can get far too many of them.
If you get lots of cultures, you'll still be limited to which ones you want strong enough because any given city can only have one culture at 50%+ at a time and for the sake of your cities struggling the least with national identity conflicts, you'll really want to make sure that all your cities are as much % of the nationally adopted culture as possible unless you're trying to prepare to change your national culture to a better, more modern one you've recently opened up. Or perhaps you're thinking of using a neighbor's national culture against him as you vie to declare YOUR nation the standard bearer of that culture by adopting the same culture they have... an interesting way to prepare to go to war so that you can assimilate the people faster perhaps.
Then again, you may want to take advantage of multiculturalism and promote some places to be more one culture than your primary cultural identity so that you can use the unique heritage history of that city to leverage it to build special buildings (like wonders or unique cultural specials) special units and heroes that those other cultures can get. New Orleans, for a real world example, could be seen to be about 20% French, 30% Creole (or Hatian), and 50% United States cultures (probably more complex than that still with some Mexican influence, some Canadian influence etc... but you get the point.) It's just a little risky to let your nation's cities start drifting towards these other cultures because of the potential for a cultural schism to be used against you or for it to potentially tear your nation in half.
Also what about the 15 limit?
That would be 'by player' as it is currently programmed. This could mean there could be 30 samurai in the world but only because you and your neighbor have been building them and both of you capped out at your alotted 15.
And if i only have like a tiny % can I make it or do I need more of an influence to build the culture units?
The unit's culture prerequisite would have to change from a boolean to an integer to reflect the % that is required for that unit to be trained. We could then set that prerequisite cultural influence for each unit as we see fit.
Most, if not all, world units requires a culture world wonder to be trained.
For regular culture units you also need to have built the respective culture world wonder.
You don't get that culture as a normal culture group in your city culture bar at all.
I'm not too fond of the culture system in place at the moment, but I have no alternative to present.
The Idea system we're discussing here is exactly my antidote for the problems this approach has come along with. It's also potentially the beginning of an entirely new approach to 'revolutions', a C2C version so to speak.
The more I think about it the more it blossoms and after a while it gets out of my ability to keep juggling my thoughts. I suppose if I slow down and think of it one piece at a time it shouldn't be so tough to design.
) is that you can build culture wonders (like before) but they take up a percentage based on when it was adopted. You can get culture percentage through trade ,age and propaganda and you need a percentage to build the unique units and there are at least 2 new civics Monoculturalism and multiculturalism, Mono increases stability but gives unhappiness and reduces great people rate based on how many cultures exist and Multi decreases stability but gives happiness and GPP based on how many cultures exist? how will this work with a tree, like what if after a few 
