Siskoni harrastaa biologiaa ja kemiaa, koska hänen tulevat opinnot liittyvät luontoon.

In Finnish, possession is often shown with a suffix instead of a separate word.

• sisko = sister
• siskoni = my sister (sisko + -ni “my”)

So -ni is the 1st person singular possessive suffix “my”.
You can also say minun siskoni, but usually people just say siskoni in normal speech and writing.

Harrastaa means “to have as a hobby / to do regularly for interest,” not simply “to study”.

• Siskoni harrastaa biologiaa ja kemiaa = My sister does biology and chemistry as a hobby / is into biology and chemistry.
• Siskoni opiskelee biologiaa ja kemiaa = My sister studies biology and chemistry (e.g. at school or university).

So harrastaa emphasizes personal interest or a hobby-like activity, not formal education.

The -aa ending here is the partitive singular.

The verb harrastaa almost always takes its object in the partitive case:

• harrastaa
  • jalkapalloa (football)
• harrastaa
  • musiikkia (music)
• harrastaa
  • biologiaa, kemiaa

So:

• biologia → biologiaa (partitive singular)
• kemia → kemiaa (partitive singular)

You do not use nominative biologia, kemia after harrastaa in this meaning.

Yes, you normally mark the case on both items linked by ja (“and”) if they both function as objects.

So you say:

• biologiaa ja kemiaa (both in partitive) not
• biologiaa ja kemia (mixed forms)

They are two separate objects of harrastaa, so both get the appropriate case ending.

Yes, that sentence is correct, but the meaning is a bit different:

• harrastaa biologiaa ja kemiaa – she is into biology and chemistry as an interest or hobby (she reads about them, follows them, tinkers at home, etc.).
• opiskelee biologiaa ja kemiaa – she studies biology and chemistry in a more formal way (school, university, courses).

In your original sentence with tulevat opinnot, using harrastaa suggests that her current hobby interests are connected with what she is going to study later.

In Finnish punctuation, you almost always put a comma before a subordinate clause starting with koska (“because”).

• Main clause, koska
  • reason clause
    Siskoni harrastaa biologiaa ja kemiaa, koska hänen tulevat opinnot liittyvät luontoon.

You can also reverse the order:

• Koska hänen tulevat opinnot liittyvät luontoon, siskoni harrastaa biologiaa ja kemiaa.

The comma is still used because koska introduces a subordinate clause in both orders.

Hänen is the genitive form of hän (“he/she”), used here as a possessive pronoun: hänen opinnot = “his/her studies”.

In this sentence, hänen clearly refers back to siskoni (“my sister”), so it means her future studies.

If you left it out and just said tulevat opinnot, it would sound more like “(the) upcoming studies” in general, not specifically her upcoming studies.
So hänen is used to make it clear that those future studies belong to your sister.

Finnish has no dedicated future tense, so it uses other means:

• Present tense with context
• Verbs like aikoa (to intend), tulla tekemään (will come to do), etc.
• Adjectives/participles like tuleva (“upcoming, future”)

Here:

• tuleva = “upcoming, future”
• tulevat opinnot = “upcoming/future studies” (plural)

So instead of a verb in a future tense, Finnish uses the adjective tuleva to give a clear future meaning.

Adjectives in Finnish agree with the noun in number and case.

• opinto = a (single) study
• opinnot = studies (plural)

Because opinnot is plural nominative, the adjective must also be plural nominative:

• singular: tuleva opinto (a future study)
• plural: tulevat opinnot (future studies)

So tulevat is just the plural form that matches opinnot.

In practice, opinnot is almost always used in the plural when you mean “studies” in general:

• opinnot = (one’s) studies (schooling, courses, academic program, etc.)

The singular opinto exists but is relatively rare and usually appears in compounds or more technical contexts (e.g. opintojakso “course unit”, opintopiste “credit”).

So hänen tulevat opinnot is the natural way to say her future studies.

Both are possible:

• hänen tulevat opinnot
• hänen tulevat opintonsa

The suffix -nsa / -nsä is the 3rd person possessive suffix (“his/her/their”).
When you already have hänen, adding the suffix is more formal and very clear:

• hänen opintonsa = definitely “his/her studies”
• hänen opinnot = also understood as “his/her studies” in modern Finnish, just a bit less formal

Your sentence with hänen tulevat opinnot is natural and common, especially in everyday language.
Hänen tulevat opintonsa would sound a bit more formal or written-style but means the same thing here.

The subject of the verb is tulevat opinnot, and opinnot is plural.
So the verb must be in the 3rd person plural:

• singular: opinto liittyy luontoon – one study is related to nature
• plural: opinnot liittyvät luontoon – the studies are related to nature

Therefore: hänen tulevat opinnot liittyvät luontoon.

Luontoon is in the illative case, which often means “into / to / toward”.

The verb liittyä (“to be connected/related to”) usually takes its complement in the illative:

• liittyä johonkin = to be related/connected to something
  • liittyä luontoon = to be related to nature
  • liittyä talouteen = to be related to the economy

So:

• luonto = nature (nominative)
• luontoon = into/to nature (illative)
• luonnosta = from nature (elative) – different meaning

That’s why luontoon is used with liittyvät here.

Yes, that is perfectly grammatical:

• Koska hänen tulevat opinnot liittyvät luontoon, siskoni harrastaa biologiaa ja kemiaa.

The meaning is the same; the difference is in emphasis:

• Original: first states what your sister does, then gives the reason.
• Reordered: first gives the reason, then tells what your sister does.

In both cases, you keep the comma between the clauses.