Eu começo a estudar música amanhã.

In European Portuguese, começar (to begin) is normally constructed with the preposition a before another verb in the infinitive. This pattern—começar a + infinitive—signals that you’re starting to do something. Without a, the sentence would be ungrammatical.

Yes. Portuguese offers three common ways to express a near future:

• Present + adverb: “Eu começo a estudar música amanhã.” (very natural in European Portuguese for planned actions)
• Periphrastic future: “Eu vou começar a estudar música amanhã.”
• Simple future: “Eu começarei a estudar música amanhã.”

Differences in nuance:
• The present + adverb is the most colloquial for tomorrow’s plans.
• “Vou começar” is clear and slightly more neutral.
• “Começarei” is more formal or literary.

No—Portuguese verbs carry clear endings that mark the subject. The -o ending in começo already tells you it’s first person singular. You can drop eu unless you want emphasis:
• Emphatic: Eu começo a estudar música amanhã.
• Neutral: Começo a estudar música amanhã.

When you study music in general (the discipline), you use the uncountable, singular form música. If you meant “pieces of music” or “individual songs,” you could use músicas. For example:
• “Vou aprender várias músicas de jazz.”

Absolutely. Portuguese word order is flexible:
• Default: Eu começo a estudar música amanhã.
• Emphatic time first: Amanhã começo a estudar música.
Both mean the same; placing amanhã up front highlights “tomorrow.”