O carro barulhento incomoda o vizinho.

Portuguese frequently uses definite articles where English might drop them. Here, O means the and specifies a particular car. You can omit or change the article to speak more generally:

• Um carro barulhento incomoda um vizinho = A noisy car bothers a neighbor (indefinite/general).
• Carro barulhento incomoda vizinho sounds incomplete or odd in European Portuguese.

barulhento is an adjective meaning noisy. In Portuguese, descriptive adjectives typically follow the noun:

• carro barulhento = noisy car.
  If you place it before (barulhento carro), it’s marked or poetic and emphasizes the adjective more strongly.

Yes. It agrees with the noun’s gender and number:

• Masculine singular: barulhento (o carro barulhento)
• Feminine singular: barulhenta (a máquina barulhenta)
• Masculine plural: barulhentos (os carros barulhentos)
• Feminine plural: barulhentas (as máquinas barulhentas)

incomoda is the third-person singular present indicative of the verb incomodar (to bother). It agrees with the subject O carro barulhento (it):

• Ele incomoda = It bothers.
  If the subject were plural, you’d use incomodam.

It’s a direct object. incomodar is a transitive verb that takes a direct object without a preposition when you say who/what is being bothered:

• O carro incomoda o vizinho (the car bothers the neighbor).

Yes. Use the passive voice with ser plus the past participle, and introduce the agent with por (by) + article:

• O vizinho é incomodado pelo carro barulhento.