Intanto che cuocio la pasta, ascolto musica in cucina.

intanto che is a conjunction meaning “while” or “in the meantime,” used to introduce a subordinate clause showing simultaneous actions.

• mentre also means “while” but is more neutral and common.
• nel frattempo is an independent adverbial phrase (“in the meantime”) and isn’t a conjunction, so you’d use it at the start of a sentence or between clauses (e.g. Nel frattempo, ascolto musica).

When you talk about an activity in general, you often omit the article in Italian.

• ascoltare musica means “to listen to music” in a generic sense.
• Adding della (ascolto della musica) would suggest you’re listening to some specific music or a particular piece.

cuocere (“to cook”) is a regular -ere verb, but its stem changes slightly in the present tense:

• The first‐person singular form is cuocio.
• This isn’t a true irregularity, just a stem adjustment.

Yes.

• mentre cuocio la pasta, ascolto musica is perfectly correct and more neutral.
• intanto che can feel slightly more colloquial or emphasize “in the meantime.”

Not if you want a single sentence linking two simultaneous actions.

• To directly connect verbs you need intanto che or mentre.
• You can say Intanto, cuocio la pasta (with a comma), but then that clause stands alone.

When naming rooms, Italian uses in without an article:

• in cucina = “in the kitchen.”
• You don’t say a cucina.

Italian often uses the definite article for foods in a general sense:

• cuocio la pasta can mean “I cook pasta” generically.
• Omitting the article (cuocio pasta) would sound unnatural.

Italian drops subject pronouns because verb endings indicate the subject.

• cuocio and ascolto are both first-person singular forms, so io (“I”) is understood but not written.