Learn Italian: A causa del chiasso, non dormo mica sodo. - Because of the racket, I do not sleep soundly at all.

In this sentence, the adjective sodo (which usually means hard or solid) is being used as an adverb to mean soundly or heavily. In Italian, some adjectives can be used in their masculine singular form as invariable adverbs. This happens frequently in specific idiomatic verb pairings, such as dormire sodo (to sleep soundly), parlare chiaro (to speak clearly), or lavorare duro (to work hard).

What is the function of mica in this sentence?

The word mica is used to strongly emphasize the negative, similar to saying at all or in the least in English. When placed after the verb, it always requires the negative particle non before the verb, just like in non dormo mica (I do not sleep at all).

Could I place mica before the verb instead?

Yes, but the grammar changes slightly. If you place mica before the verb, you must drop the non. For example, you could say ...mica dormo sodo. It means the exact same thing, but placing non before the verb and mica after it is much more common in everyday spoken Italian.

Why use A causa del instead of Perché for 'Because of'?

Perché translates to because and must be followed by a full clause containing a conjugated verb. Since chiasso (racket) is a noun, you need the prepositional phrase a causa di (because of or due to). It combines with the definite article il to form the articulated preposition del.