Why does Wilbur get all the credit?

Because the writing always described Wilbur. The first thing they see is "some pig."

Because Charlotte was doing it to save Wilbur's life. The point was for him to get all the credit. Wilbur himself does not take all he credit, just the people who see the "miracles."

Personally, I think all the animals should have been taken to the fair if the farmer knew about their singing and dancing talents.

You're right, it doesn't make sense. That occurred to me the last time I watched. Mr. Zuckerman flatout says, "There it is!" about the "grey spider," so it seems odd that all the glory would be given to Wilbur, from the standpoint of the characters, not the author (I understand she was trying to save his life, but that's not the point here).

If I had a magical spider that could weave English, I'd be pretty impressed with it...

Only Mrs. Zuckerman and Fern tried to credit Charlotte. Mrs. Zuckerman was quickly quashed by Mr. Zuckerman and Fern wasn't believed. There's probably a huge lesson there.