Estudio chino.

Spanish often drops the subject pronoun when it is clear from the verb ending.

• estudio = I study
• The -o ending already tells you the subject is I

So Estudio chino is a perfectly normal way to say I study Chinese.
You can say Yo estudio chino, but yo is usually only added for emphasis, contrast, or clarity.

Estudio is the 1st person singular present tense of the verb estudiar.

• estudiar = to study
• estudio = I study

This is a regular -ar verb, so it follows the normal pattern:

• estudio = I study
• estudias = you study
• estudia = he/she studies

It can often mean I study Chinese, and depending on context it may also be understood as I’m studying Chinese.

The Spanish present tense is broader than the English simple present. It can express:

• a habitual action: I study Chinese
• a current activity, in some contexts: I’m studying Chinese

If you specifically want to emphasize the action happening right now, Spanish often uses:

• Estoy estudiando chino = I am studying Chinese

With verbs like estudiar, hablar, aprender, and enseñar, Spanish often does not use the article before language names.

So:

• Estudio chino = I study Chinese

not usually:

• Estudio el chino

You may see the article in other contexts, especially when the language is being talked about more generally as a subject:

• El chino es difícil = Chinese is difficult

But after estudiar, leaving out the article is the normal choice.

Here, chino functions as a noun referring to the language.

In Spanish, language names are often the same form as adjectives of nationality:

• chino = Chinese
• español = Spanish
• francés = French

So in Estudio chino, chino means the Chinese language, not just Chinese as an adjective.

Yes, chino can also refer to a Chinese man, depending on context.

• un chino = a Chinese man
• una china = a Chinese woman
• chino = Chinese, the language
• comida china = Chinese food

In Estudio chino, the context makes it clear that chino means the Chinese language, because it comes after estudio.

In Spanish, names of languages are not capitalized unless they begin a sentence.

So Spanish writes:

• chino
• español
• inglés

not:

• Chino
• Español
• Inglés

This is different from English, where language names are capitalized.

A natural Spain pronunciation is roughly:

• es-TOO-dyo CHEE-no

A bit more precisely:

• estudio ≈ es-TU-dyo
• chino ≈ CHI-no

Notes:

• The stress in estudio is on tu
• The stress in chino is on chi
• ch in chino sounds like English ch in church

Not normally in this context.

The usual neutral order is:

• Estudio chino

Spanish word order is flexible, but Chino estudio sounds unnatural here unless there is some very special poetic or contrastive context.

So for a learner, the correct basic pattern is:

• verb + language
• Estudio chino
• Aprendo chino
• Hablo chino

Yes. That means I am studying Chinese and puts more emphasis on the action being in progress.

Compare:

• Estudio chino = I study Chinese / I’m studying Chinese
• Estoy estudiando chino = I am studying Chinese

The first is the more general statement. The second focuses more on the ongoing activity.

Yes. Estudio can also be a noun, depending on context.

As a noun, estudio can mean:

• study or studying
• studio
• a small apartment in some contexts

But in Estudio chino, it is clearly the verb because it is followed by chino and forms a complete sentence meaning I study Chinese.

You could, but it depends on how specific you want to be.

• Estudio chino = I study Chinese
• Estudio mandarín = I study Mandarin

Chino is the general language label.
Mandarín is more specific. If you are learning standard spoken Mandarin, mandarín may be the more precise word.