Learn Hardcore Finnish: Jään vielä hetkeksi olohuoneeseen, koska minua väsyttää. - I’ll stay in the living room for a moment longer, because I feel tired.

Jään is the 1st person singular present form of jäädä (to stay / remain / be left). In Finnish, the present tense often covers near-future intentions too, especially with context. So Jään vielä hetkeksi… naturally means I’ll stay a bit longer… (an intended action from now on), not only a timeless “I remain”.

What does vielä add here?

Vielä means still / yet / (a bit) longer. In this sentence it signals continuation: you are not leaving now; you’re staying longer than previously expected or longer than now.

Jään hetkeksi. = I’ll stay for a moment.
Jään vielä hetkeksi. = I’ll stay a bit longer (still stay) for a moment.

Why is it hetkeksi and not hetken or hetkellä?

Hetkeksi is translative case (-ksi), commonly used for duration meaning for (a period of time), especially with “stay/stop/become” type expressions.

hetki = a moment
hetkeksi = for a moment / for a while (duration)

You can also see hetken (genitive/accusative-like) used for duration, but it feels a bit different and is often more “for a (short) time” in narrative style. Hetkeksi is very common with jäädä: jäädä hetkeksi = stay for a moment.

Why is it olohuoneeseen (into the living room) instead of olohuoneessa (in the living room)? If I’m staying, I’m already there, right?

Good catch: olohuoneeseen is illative (“to/into the living room”), while olohuoneessa is inessive (“in the living room”).
Finnish allows jäädä + illative when the idea is “I’ll remain (go and remain) in that place” or “I’ll stay over in that place (rather than leaving/going elsewhere).” It can imply a choice of destination for where you will remain.

Compare:

Jään vielä hetkeksi olohuoneeseen. = I’ll stay a bit longer in the living room (often: I’ll remain here / I won’t go elsewhere).
Jään vielä hetkeksi olohuoneessa. = I’ll stay a bit longer while being in the living room (more static description of location).

Both can be used, but illative with jäädä is very idiomatic.

How is olohuoneeseen formed?

From olohuone (living room) + illative ending -eseen (because the stem ends in -e).

olohuone → stem olohuonee- → olohuoneeseen = into/to the living room
A simpler comparison:
talo → taloon (into the house)
huone → huoneeseen (into the room)

Why does it say minua väsyttää instead of olen väsynyt?

They’re two different structures:

Minua väsyttää. = I feel sleepy / I’m getting tired (literally: “sleepiness tires me”). This is an impersonal “feeling” verb pattern.
Olen väsynyt. = I am tired (a neutral state description).

Väsyttää often emphasizes the sensation coming over you (drowsiness, fatigue), similar to minua palelee (I feel cold), minua janottaa (I’m thirsty).

Why is minua in the partitive case?

With verbs like väsyttää, the person experiencing the feeling is marked in the partitive:

minua (me-PART)
sinua (you-PART)
häntä (him/her-PART)

So minua väsyttää literally treats “me” as the one affected by the tiredness. This pattern is fixed for many sensation/need verbs: minua harmittaa, minua oksettaa, minua nukuttaa, etc.

Does koska always mean “because”? Can it mean “when” too?

Koska most commonly means because. It can mean when in some contexts, but that’s less common and usually clearer from the surrounding sentence. Here it’s unambiguously because, since it gives a reason: …, koska minua väsyttää.

What’s the basic word order here, and can it change?

Neutral order:

Jään (verb) vielä hetkeksi (time) olohuoneeseen (place), koska (because) minua väsyttää (reason).

You can move parts for emphasis:

Koska minua väsyttää, jään vielä hetkeksi olohuoneeseen. (Reason first, slightly more formal/structured.)
Olohuoneeseen jään vielä hetkeksi, koska minua väsyttää. (Emphasizes the place.)

Finnish word order is flexible, but changes usually signal emphasis or topic.

Is this sentence more written Finnish or spoken Finnish? How would it sound in everyday speech?

It’s standard, natural Finnish (fine in both writing and speech). In casual spoken Finnish you might hear:

Jään vielä hetkeks olkkariin, ku mua väsyttää. Changes:
hetkeksi → hetkeks (final vowel often reduced)
olohuoneeseen → olkkariin (slang for “living room”)
koska → ku (common spoken “because”)
minua → mua (spoken form)

How would I negate it?

Negation uses the Finnish negative verb en:

En jää vielä hetkeksi olohuoneeseen, koska minua ei väsytä. = I won’t stay a bit longer in the living room because I’m not sleepy.

Notes:

Main clause: en jää (negative + verb in connegative form)
In the väsyttää clause, you negate with ei: minua ei väsytä (“I don’t feel sleepy”).