Is well an adverb

It depends how it is used. Well is an adverb for something done well. The adjective form is usually "good."

See the examples below:

Did you sleep well? (adverb - in a good fashion)

She isn't feeling well today. (adjective - not ill) *modifies she

Well! I see you are late for school again. (interjection)

He threw a coin into the well. (noun - water hole)