Learn Hardcore Finnish: Otan punaisen takin, koska ulkona on kylmä. - I take the red coat because it is cold outside.

In Finnish, when a noun is the object of a complete (telic) action, it usually appears in the accusative form, which for singular nouns looks like the genitive. Here:

takki (nominative) → takin (genitive/accusative singular)
The adjective must agree in case, so punainen → punaisen.
Thus punaisen takin literally marks “the whole red coat” as the direct object of otan (“I take”).

How do I decide between the genitive/accusative (takin) and the partitive (takkia) for the object of ottaa?

Finnish distinguishes:

Partitive (e.g. takkia) for incomplete, ongoing, indefinite or partial actions (“I’m taking some coats,” or “I’m taking at least part of the coat”).
Accusative/genitive (e.g. takin) for complete, one-off, definite actions (“I take the coat and that’s it”).
Since otan punaisen takin implies you take exactly one red coat (a bounded event), the genitive/accusative is correct.

Why is ulkona used here? What case is it, and could I use ulos or ulkopuolella instead?

ulkona is the adessive case (noun + -na/-nä) meaning “at the outside,” i.e. “outside (as a location).”
ulos means “out (movement towards the outside),” so you’d use it with verbs of motion (“I go out” → mennä ulos).
ulkopuolella (“outside of”) is possible, but rarer in colloquial speech: ulkopuolella on kylmä sounds more formal or technical.
For a simple weather statement, ulkona on kylmä is the normal choice.

Why is there a comma before koska? Can I drop it?

In Finnish, when a subordinate clause (here introduced by koska) follows a main clause, it’s standard to separate them with a comma:
Otan punaisen takin, koska ulkona on kylmä.
If you drop the comma, the sentence still remains understandable, but punctuation rules recommend marking that boundary. If the koska-clause comes first, you don’t need a comma afterward.

Could I use sillä instead of koska for “because”?

koska introduces a subordinate causal clause (“…because it is cold outside”).
sillä is a coordinating conjunction linking two main clauses, typically at the start:
Sillä ulkona on kylmä, otan punaisen takin.
You cannot place sillä at the end of a sentence like Otan punaisen takin sillä ulkona on kylmä—that would be ungrammatical.

Why is the subject minä omitted in Otan?

Finnish verbs carry person and number endings, so the subject pronoun is often unnecessary:

otan = “I take” (1 sg.)
Since the verb form already tells you who does the action, native speakers drop minä unless they want to emphasize “I” specifically.

Is the word order koska ulkona on kylmä fixed? Could I say koska on kylmä ulkona or ulkona on kylmä, koska…?

Finnish word order is relatively flexible:

koska ulkona on kylmä is the most neutral for a subordinate clause.
You could say koska on kylmä ulkona, but it shifts emphasis slightly onto kylmä, making ulkona feel like an afterthought.
And yes, if you wanted a stylistic variation, you can start with Ulkona on kylmä, koska and then continue the main clause, though putting the because-clause after the main clause (with a comma) is far more common.