En cuanto termino mi tarea, ceno con mi familia.

Because the speaker is describing a habitual or routine action. In Spanish, when you talk about something you always do, you use the present indicative in both clauses:

• En cuanto termino mi tarea, ceno con mi familia.
  If you were referring to a specific future event (not a routine), you’d use the subjunctive in the subordinate clause and future in the main clause:
• En cuanto termine mi tarea, cenaré con mi familia.

Yes, when the adverbial clause comes first, it’s standard to separate it with a comma from the main clause. It makes the sentence clearer:

• En cuanto termino mi tarea, ceno con mi familia.
  If you flip the order—Ceno con mi familia en cuanto termino mi tarea—you typically drop the comma.

Ceno is the first person singular of cenar, meaning “I have dinner.” It reflects the speaker’s personal routine. If you want to say “we have dinner,” you’d use cenamos:

• En cuanto termino mi tarea, cenamos con mi familia.

Yes. All three introduce temporal clauses, but with slight nuance:

• En cuanto and tan pronto como both stress immediacy.
• Cuando is more general (“when”).
  Examples:
• Tan pronto como termino mi tarea, ceno con mi familia.
• Cuando termino mi tarea, ceno con mi familia.

Both mean “homework,” but usage varies by region:

• Tarea is more common in Latin America.
• Deberes is more frequent in Spain.

You can, but that uses the present subjunctive acabe to talk about a not-yet-completed action. It shifts from a habitual routine to a single, upcoming event. You’d normally pair it with a future main verb:

• En cuanto acabe mi tarea, cenaré con mi familia.