No. School is a noun, or colloquially a verb (to teach). It can be considered an adjunct or adjective, as in school days, school campus.
No. Adverb phrases are often used instead (in school, of school, concerning school).The word school is often used as an adjective/ noun adjunct (school subjects, school uniform), but there is no adverb form. The generally synonymous adjective scholastic and adverb scholastically are often used, which are based on the noun scholar.
The adverb is quickly.
The adverb of the sentence is quickly.
The adverb is "outside". It is an adverb of place, describing where they were playing.
No, it is not an adverb. Graduation is a noun, typically used to mean completion of education (high school, college).
No, it's a verb. "John attended school."
Regularly
No. Steady is an adjective. The adverb form would be steadily.
Yes, the word 'recently' is an adverb because it alters the meaning of a verb. An example would be 'he recently had the flu and was unable to go to school' where had/have is the verb.
No, there is no adverb form of skipping. The word skipping is the present participle of the verb to skip. Well, it may or may not be an adverb depending upon the usage if the work "skipping" answers questions such as "how," "when," "where," "how much" in that scenario it would be an adverb. So, in the sentence I am skipping. Skipping is clearly not an adverb, but in a sentence like I went to the school skipping, skipping is an adverb
No. It is a plural noun, or less frequently a verb form (as in "he motorcycles to school").