Learn Hardcore Finnish: Nuori muusikko opiskelee suomea kotona. - The young musician studies Finnish at home.

Nuori muusikko can mean a young musician or the young musician depending on context.
The language relies on word order, context, and sometimes demonstratives (like tämä = this, se = that) to express definiteness when it really matters.

So the sentence is correct and complete without any article word.

Why is the order nuori muusikko and not muusikko nuori?

In Finnish, adjectives normally come before the noun they describe, just like in English:

nuori muusikko = a young musician
vanha talo = an old house
suuri koira = a big dog

Also, the adjective agrees with the noun in case and number. Here, both are nominative singular:

nuori (nominative singular)
muusikko (nominative singular)

If the noun changed case, the adjective would change too, e.g.:

nuorta muusikkoa = (partitive singular) a/ the young musician (as object/partitive)

What form is muusikko, and why?

Muusikko is in the nominative singular, which is the basic dictionary form of a noun and is used for the subject of a simple sentence.

Subject: Nuori muusikko
Verb: opiskelee
Rest of the sentence: suomea kotona

So muusikko is nominative singular because it is the subject (the one doing the studying).

Why isn't there a pronoun like he or she (hän) in the sentence?

In Finnish, a subject pronoun like hän (he/she) is often omitted when it is clear from context who is doing the action and there is another subject present in the sentence.

Here, nuori muusikko is already the subject, so adding hän would be redundant and sound odd:

Natural: Nuori muusikko opiskelee suomea kotona.
Odd / redundant: Hän nuori muusikko opiskelee suomea kotona.

However, if the subject were only a pronoun, you would use it:

Hän opiskelee suomea kotona. = He/She studies Finnish at home.

What is the verb opiskelee exactly, and how is it formed?

Opiskelee is the 3rd person singular present tense of the verb opiskella (to study).

The pattern for opiskella (type 3 verb) in the present tense is:

minä opiskelen (I study)
sinä opiskelet (you study, singular)
hän opiskelee (he/she studies)
me opiskelemme (we study)
te opiskelette (you study, plural/formal)
he opiskelevat (they study)

Notice how the stem opiskele- stays, and personal endings are added. For hän, the ending is -e, which combines with the stem vowel to give opiskelee.

Also, this one Finnish present tense covers both English studies and is studying:

Nuori muusikko opiskelee suomea kotona.
= The young musician studies Finnish at home / is studying Finnish at home.

Why is it suomea and not suomi in this sentence?

Suomea is the partitive form of suomi (Finnish language). Many verbs that describe studying, learning, speaking, knowing, liking a language take the object in the partitive case.

Compare:

Nominative: suomi (dictionary form)
Partitive: suomea

With opiskella (to study), the thing you study is typically partitive, because it is seen as an ongoing, incomplete or not fully delimited activity:

opiskella suomea = to study Finnish (in general, as an ongoing process)
puhua suomea = to speak Finnish
ymmärtää suomea = to understand (some) Finnish

You would not normally say opiskella suomi; that sounds wrong to native speakers.

What does the ending -a in suomea mean exactly?

The -a/ä ending (with other variations) is one marker of the partitive case. The partitive is used a lot in Finnish; some typical uses:

For indefinite or partial objects (not seen as a complete whole)
With many verbs of feeling, liking, speaking, learning, studying, etc.
With expressions of quantity or some amount

Here, suomea is:

Partitive singular of suomi
Function: object of the verb opiskelee

So grammatically:
Nuori muusikko (subject, nominative)
opiskelee (verb)
suomea (object, partitive)
kotona (adverbial of place, inessive)

What does kotona mean exactly, and why does it end in -na?

Kotona means at home.

The base noun is:

koti = home (noun, nominative)

Finnish has a set of local cases that express location. For koti:

kotiin = to home (movement towards; illative)
kotona = at home (location inside/at; inessive form of this irregular stem)
kotoa = from home (movement away; elative)

The ending -na here is part of a special inessive form for koti; historically related to -ssa/ssä (the usual inessive), but you just need to memorize kotona as the standard way to say at home.

So:

Olen kotona. = I am at home.
Menen kotiin. = I go home.
Tulen kotoa. = I come from home.

Can I change the word order, and if so, what changes?

Yes, Finnish word order is fairly flexible, and changes mainly emphasis or what is new information, not the basic meaning. Some possibilities:

Nuori muusikko opiskelee suomea kotona.
Neutral: subject first, typical statement.
Kotona nuori muusikko opiskelee suomea.
Emphasis on where: At home, the young musician studies Finnish.
Suomea nuori muusikko opiskelee kotona.
Emphasis on what: It’s Finnish that the young musician studies at home (not another language).

The core relations (who studies what where) don’t change; you just highlight different parts of the sentence. The original order is the most neutral.

Why is suomea not capitalized, while Finnish is capitalized in English?

In Finnish, names of languages and nationalities are not capitalized unless they start a sentence.

suomi = Finnish (the language)
englanti = English
ruotsi = Swedish

So in the middle of a sentence:

Hän opiskelee suomea. = He/She studies Finnish.

Only proper names like country names, cities, people, etc., are capitalized:

Suomi = Finland (the country, capitalized)
suomi = Finnish (the language, lowercase)

What’s the difference between double letters like in muusikko and single letters?

In Finnish, double consonants and double vowels are meaningful; they change the pronunciation and can change the meaning of a word.

muusikko = musician (uu is a long vowel, kk is a long consonant)
musiikko or musiko would be wrong spellings and sound clearly different.

Some examples of contrast:

tuli = fire
tuuli = wind
muta = mud
mutta = but

So you need to pay attention to double letters when reading and writing Finnish; they are not just spelling details, they are part of the word’s identity.

Does opiskelee mean studies or is studying, or both?

Both. Finnish does not have a separate continuous tense like English am/is/are studying.

The present tense (here: opiskelee) can correspond to:

He/She studies Finnish at home. (habitual or general)
He/She is studying Finnish at home. (right now / around this time)

Context usually tells you whether it’s a general habit or something happening now. The Finnish sentence itself doesn’t mark that difference.