Is "a" an adjective?
No. Word "a" is not an adjective. It is an indefinite article.
Articles (a/an and the) don't describe the nouns, don't add any extra information.
If I say I ate an apple, I don't say anything special about the fruit I ate. To add any information I have to use adjectives. For example in a sentence I ate a sweet apple word a does not give any information about the fruit unlike adjective sweet which describes the apple.
Articles are used only to inform the reader if we speak generally or about one specific thing.