In a movie I heard an actor saying "I'm dead serious". I looked up the dictionary and found that "dead" in this context means "really". Is it formal? Can we use it in business meetings?
Dead, as adverb, is informal when used to mean very, such as in "omelets are dead easy to prepare." (As far as I know, dead is used to mean very only in British English.)
When dead is used to mean absolutely, completely, exactly, straight, or directly it is not used only in informal phrases.
Well, the use of a contraction isn't formal, but putting that aside …
Since the intended meaning of the word in that phrase does match the literal definition of dead as an adverb, it must technically be considered formal. However, such usage is certainly secondary to its common interpretation as a noun, and is liable to confuse your audience across cultural and language barriers. In formal writing, I'd avoid it just in case the people judging your work falsely condemn it.
Neither is the phrase offensive, but the primary meaning of dead still lends it a slightly morbid connotation. I'd use it sparingly and in appropriate context. For example, I'd say I'm dead serious in a business meeting, but not you're dead right. The latter statement clashes with the adverb's connotation, which makes the word stand out rather than just effectively carry your thoughts.
It should be used sparingly in formal settings(if you keep saying "dead" you will creep out people), but it isn't offensive and it isn't inappropriate to use when you really need to.
So it isn't the most formal, as it exaggerates meaning.