Чё

This word is a synonym of что?

That's not a synonym of что, it's just how что is often pronounced in day-to-day speaking. Note: if что is a conjuction, then don't say чё, say што. If you need to speak all formal, don't say чё either.

"чё те надо?" = "что тебе надо?"
"чё ваще?" = "что вообще?"
vulgar forms.

Чё is used instead of both что and чего.

It's wha' .... Что is full form, чё is fast and contracted and in most contexts impolite (but sometimes it's appropriate).