New Amsterdam seems to have been somewhat of a melting pot, much like it´s successor New York. Did the colony develop it´s own (mixed) culture in her 40 years of existence? Or did it closely resemble Dutch society?

Dutch culture did hang on for a while, but English settlers ended up outnumbering the Dutch. I read somewhere once (I would have to track it down) that Albany was as Dutch-speaking as it was English up to 1800, and lots of Hudson Valley towns still have an old Dutch church that is still open and in use. Martin Van Buren, who grew up in Kinderhook, was the only American president to have grown up speaking a language other than English. The wealthy old Dutch families were at the top of society in a lot of that area up into the mid-1800s, and a handful, like the Roosevelts, kept their money and power longer than that.

After the Revolution, there was a big wave of New England Yankee war veterans who moved to Upstate New York. That's probably what doomed the Dutch demographically.