For eg. He said " He would go for a movie". ? Or John said " I could or (would like to) eat the cookies "
It depends on the context. If those are the exact words used by the speakers then they are fine. The first sounds more like indirect speech:
"I will go to the cinema, " said John.
John said he would go to the cinema.
However, there are no restrictions on what people say, so if he used the words He would go for a movie then it is correct. Are you trying to use direct or indirect (reported) speech?
I'm trying these tenses in Direct speech like John said " He would like to eat cookies". The one that comes within inverted commas is Direct speech. Right ?
The words "He would like to eat cookies" are indeed direct speech, and there are contexts in which this sentence is grammatically correct. There are far fewer contexts in which the words "He would go for a movie" are possible.