Learn Hardcore Finnish: Olen ylpeä siskostani, koska hän on hyvin itsenäinen. - I am proud of my sister because she is very independent.

So Olen ylpeä… already clearly means I am proud….
You can say Minä olen ylpeä… as well, but it usually adds emphasis on minä (e.g. I am proud, maybe in contrast to someone else).

In neutral, everyday sentences, the version without minä is more typical in written Finnish.

Why is it siskostani and not just sisarestani or something like that?

The word siskostani is made from:

sisko = sister (colloquial, very common)
siskosta = from/of (my) sister (elative case: -sta / -stä)
siskostani = from/of my sister (-ni = my)

So structurally: sisko + sta + ni → siskostani.

Why -sta / -stä (elative case)? Because the adjective ylpeä (proud) is normally followed by the elative when you say proud of someone:

Olen ylpeä siskostani. = I am proud of my sister.
Olen ylpeä lapsestani. = I am proud of my child.
Olen ylpeä sinusta. = I am proud of you.

This is just how Finnish expresses “proud of X”:
ylpeä + elative case (jostakusta / jostakin).

Sisarestani would be from sisar (sibling / (female) sibling), which is more formal or written; sisko is the normal everyday word.

What exactly does the -ni in siskostani mean, and can I also say minun siskostani?

The suffix -ni on a noun is a possessive suffix meaning my.

sisko = sister
siskoni = my sister
siskostani = from/of my sister

So siskostani literally has the “my” built in.

You can also add a separate possessive pronoun:

Minun siskostani = of my sister
Olen ylpeä minun siskostani.

This is grammatically correct, but in neutral style you usually choose either:

Olen ylpeä siskostani. (suffix only)
or
Olen ylpeä minun siskostani. (pronoun only – more spoken style or for emphasis)

Using both (minun siskostani) with -ni (siskostani) together is possible but sounds strongly emphatic or clumsy in many contexts.

Why is it siskostani and not siskoni after ylpeä?

Some adjectives in Finnish “govern” a specific case after them. Ylpeä is one of these: it normally takes the elative (-sta / -stä).

ylpeä jostakusta / jostakin = proud of someone / something

So:

Olen ylpeä siskostani. = I am proud of my sister. (correct, natural)
Olen ylpeä siskoni. – feels incomplete/wrong, like saying I am proud my sister without the “of”.

Think of ylpeä as if it almost requires a “from/of” meaning in Finnish, which is expressed by the elative (siskosta, lapsesta, sinusta, etc.).

Could I put the koska-clause at the beginning, like in English: “Because she is very independent, I am proud of my sister”?

Yes. Finnish allows both orders:

Olen ylpeä siskostani, koska hän on hyvin itsenäinen.
Koska hän on hyvin itsenäinen, olen ylpeä siskostani.

The meaning is the same.
When the koska-clause comes first, you must use a comma between the clauses, just like in the original sentence.

Word order is relatively flexible in Finnish, so both versions are natural.

What is the difference between koska and other words like sillä or että for “because”?

All three can relate to reasons, but they are used differently.

koska = because (neutral, very common in both spoken and written language)
- Olen iloinen, koska hän tuli. = I am happy because she came.
sillä = for / because (more written, explanatory, often slightly formal)
- Olen iloinen, sillä hän tuli.
  Sounds like giving an explanation in a written argument or essay.
että usually means that, not because.
- Tiedän, että hän on itsenäinen. = I know that she is independent.

You cannot replace koska with että in this sentence.
You could use sillä in certain more formal or narrative contexts, but koska is the most natural here.

Why is it hän and not a separate word for “she”? Does hän mean both “he” and “she”?

Yes. Hän is a gender-neutral third-person singular pronoun:

hän = he / she
hänen = his / her

Finnish does not have separate words for “he” and “she”. Context usually tells you whether hän refers to a man, a woman, or just a person without focusing on gender.

In Olen ylpeä siskostani, koska hän on hyvin itsenäinen, we know from siskostani (my sister) that hän refers to a female person, but grammatically hän itself is genderless.

In casual spoken Finnish, people often use se (literally “it”) instead of hän:

Mä oon ylpee mun siskosta, koska se on tosi itsenäinen. (spoken)

Does hyvin here mean “well” or “very”? Could I use something like tosi or erittäin instead?

Hyvin can mean both:

well
- Hän puhuu suomea hyvin. = She speaks Finnish well.
very (especially before adjectives)
- Hän on hyvin itsenäinen. = She is very independent.

In this sentence it clearly means very.

You can also use:

tosi itsenäinen = really independent (informal)
todella itsenäinen = really / truly independent (neutral)
erittäin itsenäinen = very / extremely independent (a bit more formal or stronger)

All of these would be understood:

hän on tosi itsenäinen
hän on todella itsenäinen
hän on erittäin itsenäinen

Hyvin is a safe, neutral choice, especially in written Finnish.

Why is ylpeä in this form? Should it change to match something, like plural or case?

Here ylpeä is a predicative adjective: it describes the subject through the verb olla (to be).

For a singular subject, you use the basic form (nominative singular):

(Minä) olen ylpeä. = I am proud.
(Hän) on ylpeä. = He/She is proud.

If the subject is plural, the adjective usually becomes plural too:

(Me) olemme ylpeitä. = We are proud.
(He) ovat ylpeitä. = They are proud.

So:

Olen ylpeä siskostani. — 1 person, ylpeä
Olemme ylpeitä siskostamme. — more than 1 person, ylpeitä

The case of the noun after it (siskostani) is determined by the adjective’s pattern (ylpeä + elative), but ylpeä itself stays in nominative because it is the predicative after olla.

What kind of word is itsenäinen, and how does it behave grammatically?

Itsenäinen is an adjective meaning independent. It behaves like a regular -inen adjective.

Basic forms:

singular nominative: itsenäinen
singular genetive: itsenäisen
plural nominative: itsenäiset
plural partitive: itsenäisiä

With olla:

Hän on itsenäinen. = She/he is independent.
He ovat itsenäisiä. = They are independent.

In your sentence, hän on hyvin itsenäinen, itsenäinen is in the basic (nominative) form describing the subject hän.

How would this sentence look in very casual spoken Finnish?

A typical colloquial version might be:

Mä oon ylpee mun siskosta, koska se on tosi itsenäinen.

Differences from the standard form:

Minä → Mä (spoken I)
olen → oon
ylpeä → ylpee (vowel reduction)
siskostani → mun siskosta (mun = my, no possessive suffix)
hän → se (spoken he/she)
hyvin → tosi (very/really, informal)

The original sentence you gave is in standard written Finnish, which is what you should learn first; the spoken version is useful to recognize in real-life conversations.