Learn Italian: Il giudice ha deciso di accogliere il ricorso. - The judge decided to grant the appeal.

When the verb decidere (to decide) is followed directly by an infinitive verb, it requires the preposition di. This is a set pattern you have to memorize: decidere di fare qualcosa (to decide to do something).

Accogliere normally means to welcome or receive. Why is it translated as grant here?

In Italian legal and formal contexts, accogliere is the standard verb used to mean accepting, upholding, or granting a request, such as an appeal (il ricorso). You can think of it as the court formally welcoming the petition.

Since we are learning about impersonal passives, how would I change this sentence to say It was decided to grant the appeal?

You would use the impersonal construction si è deciso di accogliere il ricorso. Even though decidere normally takes avere in the active voice, impersonal constructions with si always use essere as their auxiliary verb, conjugated here in the third-person singular.

How do you know giudice is masculine? Does the word change if the judge is a woman?

Nouns ending in -e do not change their ending for gender. If the judge were a woman, the noun would stay exactly the same, but the article would change to feminine: la giudice. In this sentence, il tells us the judge is either male or being referred to generically.