Is sleep a noun

Answer 1

The word 'sleep' is both a verb and a noun. Examples:

I usually sleep all night. - verb

My father would tell us that the sleep you get before midnight is the sleep that counts. - noun

Answer 2

Yes, the word 'sleeping' is a gerund, the present participle of the verb to sleep that functions as a noun in a sentence. The present participle of the verb also functions as an adjective.

Examples:

I often wear a mask for sleeping. (noun, object of the preposition 'for')

I was sleeping when you called. (verb)

A sleeping cat lay in the sunlight. (adjective)