1. Did Spanish uses Carracks too? (did they call it Nau/Nao?) I've read somewhere that Spanish Armada headed to England consists of: War Galleons (25-50 guns), Carracks, Nau, Four Italian Galleasses, and armed merchant holks
2. Galleons also prove popular in Europe. English quickly improved galleon designs and make a Manowar. also used alongside war carracks. Dutch De Zeven Provincien is also super galleon (70 guns or so).
3. So for how long did Caravels, Carracks and Nau, and Galleons remain in use? when did Dutch, French and British design supercede these Renaissance designs? did Dutch creates armed yatchs and how well did it performs both at seagoing and combat?
UF! These questions are far beyond my knowledge of the topic

I will give you my opinion but maybe someone know the answer better!
And take some of them with caution as I can be not right!
1. As far as I know, yes they did. In Spanish “Nao" means literally "ship" and normally used for Big Ships. The word is old, now "barco" it is used instead for the same meaning of "big ship", but both are correct and you can use it). During the XV century (some centuries before and some after) "nao" was also a model of ship that was different from the caravel, the carrack and the galleon.
It was similar to the carrack but with lower deck and without a castle in the front (the ship was more "plain" so to speak).
For example, a Carrack or a galleon could be called "nao" but they didn't had to be a "Nao" if we understand them as the model.
The manila Galleon, was made by galleons but they were known as "Nao de china" (The ship from China) meaning the ship that did this journey. But it was a Galleon, not a "nao", the ship that had his own characteristics as a ship.
Therefore, Carracks could be called naos as they were big ships.
In the picture I posted, the Santa María was a Nao (model of the ship) but the other 2 were not (Caravels). The 3 of them could be called "Naos" as they 3 big ships.
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For the armada, I do not know the exact different ships that made part of the armada, but for sure they had galleons that were transformed for military use, Carracks, Naos, pinnaces, Urcas, and ZXX
This ships came along from all parts as the armada was made by ships from all the kingdoms; Castile, Portugal (as they were considered among the (if not the) best ships the Flagship was a Portuguese gallion), Aragon, Basque Country, etc..
So it's normal that it was a mixture for all kind of ships, as the ships that came from Basque country where more suited for coast vigilance (Patache and pinnaces), the ones from Castile were galleons, Portuguese had carracks and galleons, Italian had galleasses being in the middle of Mediterranean see, etc.
Of course, all countries had a little of every kind of ships for different purposes.
2) As for the evolution of carracks and naos, every country did improvements according to their needs. For example, the English galleon was lower, and with more guns as the Spanish were taller and less armed. Why?
During this period, Spain had to transport all the goods from and to the intercontinental colonies (as explained in the other post) so the Spanish galleon was a perfect ship for this role. Spaniards were also more suited for boarding combat (therefore the high of their galleons), English continued the Portuguese trend to add more cannons to sink the enemy before boarding. The English during xvi and xvii had little to transport so no need of big cargo.
The Spanish galleons suffered for their "multipurpose" capacity:
- Very good commercial ship
-Very good combat ship
However, the English galleon was more suited for combat in open waters as it was more maneuverable (smaller, and lower) and had better firepower (no cargo = the extra space to cannons).
- Average/good commercial ship
-Excellent combat ship
3) I do not know when the different designs turned obsolete. I think is very hard to know, as a lot of model where used for a long time.
For example, the pinnaces were used, already, in the xiii century but the ship model was part of the spanish armada of the Xvi century. For sure, they were upgrade with the new ideas of navigation but that illustrate how difficult is to now that.
Manowars were the evolution of the English galleon. Now, they just removed the cargo ability and they centered into have more cannons and armament, and the roles for trade went to ships centered in this purpose.
So a manowar is better in combat that a galleon but worst for trade, and a merchant ship like an Urca is better for trade than a galleon but worst in combat. They just specialized the ships in a concrete purpose.
During XVIII century until middle of XIX, transport and commerce was made by armadas mixing Commercial ships and Manowar for defense (if the ships of the line were destroyed or fled, the transport ships were doomed).
Like in the examples of:
- The action of 9 august
https://en.wikipedia.org/wiki/Action_of_9_August_1780
- The battle of Cape of finisterre finisterre
https://en.wikipedia.org/wiki/Second_Battle_of_Cape_Finisterre_(1747)
Both actions show how, now with the new system, the merchants were totally dependent on the Military vessels and incapable of defending themselves.
So as everything, is not that a model is better than another is. Normally, everything (including ships) evolve to adapt to new necessities or particular circumstances.
Another example, and I will try to answer about the Dutch vessels, they used a lot the frigates. These were very useful in "low" waters like in the coast and some interiors of northern Europe. So, similar in purpose to the English galleons but more suited to the Dutch idiosyncrasy.