Could this be used in a sarcastic sense, like, "Wow, look what you did. Are you happy now?"
Yes, it can.
Nöjd is kinda the opposite of annoyed. :)
Doesn't ''nöjd'' also mean ''pleased''?
I thought so too.
I think satisfied and pleased often mean the same thing in English. E.g. 'I was pleased/satisfied with the design.'
Is that where the word for the amusement park 'nöjesfältet' comes from?
They're closely related, yes. Nöje means "amusement, pleasure, delight" and fält means "field".
Cant "nöjd" also mean "content"?
Yes it can.
Why doesn't it accept "Are you pleased now"?
It could be useful to understand what is the exact scope and meaning of the word "nöjd" ( satisfied / contented /etc )... in swedish