Learn Spanish (Latin America): Habiendo visto la sentencia, el abogado apeló el miércoles. - Having seen the sentence, the lawyer appealed on Wednesday.

It sets the background timeline, showing that the action of "seeing" was completely finished before the main action (apeló) took place. While you could also say después de ver la sentencia (after seeing the ruling), using the perfect gerund habiendo visto strongly emphasizes the cause-and-effect relationship: because he had seen it, he appealed.

Does sentencia mean a grammatical sentence here?

No, in Spanish sentencia is a "false friend" when talking about grammar. It strictly refers to a legal verdict, ruling, or court sentence. If you want to talk about a sentence in a paragraph or language lesson, you must use oración or frase.

Why use the preterite apeló here instead of the imperfect apelaba?

The act of appealing was a specific, completed event that took place on a specific day (el miércoles). The imperfect apelaba would imply a continuous, background, or habitual action in the past (like "he was appealing" or "he used to appeal"), which doesn't fit this single completed action.

Why does the sentence use el miércoles for "on Wednesday" instead of translating the word "on"?