All the unique improvements as mentioned still need to be looked at. (Except Terrace Farm and Polder maybe?).
Main problem is the culture balance, easiest would probably be comparing them to the tradingpost, which gives something like 4 gold 1 science 1 culture (1 faith?)
Comparing a 3 gold 3 culture chateau with that is pretty fair, the chateau is about equal, if not a little better. The issue however is that in the basegame the chateau is a lot better than any alternative improvement and is balanced with that in mind(placement requirements).
For the others you kinda need to assume that 1 culture is worth something like 3 gold for them to stay relevant.
Easy(but boring) solution would be to give them all the tradingpost policy bonuses, 1gold from currency, 1 science from knowledge and 1 culture from aesthetics, (1 faith from Religious settlements maybe?). No clue if that would be balanced however, the chateau would end up with 4 gold 4 culture and 1 science (1 faith?), The brasilwood camp would have 3 gold 3 culture 1 science (1 faith?).
The maoi however I have no clue about, I never play polynesia.
The terrace farm is fine, really no need to change anything about it.
The Polder I would still argue should have a freshwater access bonus at Civil service, just to keep it consistently better than a farm. (This would ofc change the bonus at Fertilizer to only give extra food to polder-tiles without freshwater access)
The Kasbah is a lot trickier however. One could either try and keep it unique by just giving it some bonus(that I can't think of tbh.) later on, but that would be a lot of work.
My easier solution would be just to decide what kind of baseimprovement it should be and just give it all those existing bonuses.
You could make it a Farm, a Mine or a Tradingpost without too much trouble I think.
What I mean is that while it would still have the desert only requirement you could either make it a farm with all the existing farmbonuses (And the base 1 production 1 gold),
a mine with all the existing minerelated bonuses (and +1 food +1 gold) or
a tradingpost with all the existing tradingpost bonuses (+1 food 1+ production)
This would however make the kasbah pretty damn strong, sure on flat desert-tiles a tradingpoststyle-kasbah would just be like a tradingpost on plains, not very impressive, on a deserthill or floodplain however that would have 2 extra hammers or 2 extra food which would be pretty powerful (So you would maybe need to put additional tile-requirements on it), however unique improvements are meant to be good, I'm just not sure how good.
In my opinion the Farm-style-kasbah or the tradingpost-style-kasbah makes most sense gameplayvise, a mine would be more unique because there are no mine-replacements.
End pruduct would be something like this(assuming you've gone for every existing bonus, which isn't really realistic):
TP-style-Kasbah: 1 food 1 production 4 gold 1 science 1 culture (1 faith?)
Farm-style-kasbah: 3 food 1 production 1 gold. (assuming you went freedom ofc)
Mine-style-Kasbah: 1 food 4 production 1 gold (assuming you went order)
Main problem is the culture balance, easiest would probably be comparing them to the tradingpost, which gives something like 4 gold 1 science 1 culture (1 faith?)
Comparing a 3 gold 3 culture chateau with that is pretty fair, the chateau is about equal, if not a little better. The issue however is that in the basegame the chateau is a lot better than any alternative improvement and is balanced with that in mind(placement requirements).
For the others you kinda need to assume that 1 culture is worth something like 3 gold for them to stay relevant.
Easy(but boring) solution would be to give them all the tradingpost policy bonuses, 1gold from currency, 1 science from knowledge and 1 culture from aesthetics, (1 faith from Religious settlements maybe?). No clue if that would be balanced however, the chateau would end up with 4 gold 4 culture and 1 science (1 faith?), The brasilwood camp would have 3 gold 3 culture 1 science (1 faith?).
The maoi however I have no clue about, I never play polynesia.
The terrace farm is fine, really no need to change anything about it.
The Polder I would still argue should have a freshwater access bonus at Civil service, just to keep it consistently better than a farm. (This would ofc change the bonus at Fertilizer to only give extra food to polder-tiles without freshwater access)
The Kasbah is a lot trickier however. One could either try and keep it unique by just giving it some bonus(that I can't think of tbh.) later on, but that would be a lot of work.
My easier solution would be just to decide what kind of baseimprovement it should be and just give it all those existing bonuses.
You could make it a Farm, a Mine or a Tradingpost without too much trouble I think.
What I mean is that while it would still have the desert only requirement you could either make it a farm with all the existing farmbonuses (And the base 1 production 1 gold),
a mine with all the existing minerelated bonuses (and +1 food +1 gold) or
a tradingpost with all the existing tradingpost bonuses (+1 food 1+ production)
This would however make the kasbah pretty damn strong, sure on flat desert-tiles a tradingpoststyle-kasbah would just be like a tradingpost on plains, not very impressive, on a deserthill or floodplain however that would have 2 extra hammers or 2 extra food which would be pretty powerful (So you would maybe need to put additional tile-requirements on it), however unique improvements are meant to be good, I'm just not sure how good.
In my opinion the Farm-style-kasbah or the tradingpost-style-kasbah makes most sense gameplayvise, a mine would be more unique because there are no mine-replacements.
End pruduct would be something like this(assuming you've gone for every existing bonus, which isn't really realistic):
TP-style-Kasbah: 1 food 1 production 4 gold 1 science 1 culture (1 faith?)
Farm-style-kasbah: 3 food 1 production 1 gold. (assuming you went freedom ofc)
Mine-style-Kasbah: 1 food 4 production 1 gold (assuming you went order)