Huomenna pyykkivuoro on kello kahdeksalta, joten herään aikaisin.

Pyykkivuoro is a compound word:

• pyykki = laundry
• vuoro = turn, shift, slot, reserved time

So pyykkivuoro means something like a laundry slot or my turn to do laundry. In Finland, this often refers to a reserved time in a shared laundry room in an apartment building.

Because Finnish word order is quite flexible. Starting with Huomenna puts the time first and gives it emphasis.

So:

• Huomenna pyykkivuoro on kello kahdeksalta
  = Tomorrow, the laundry slot is at eight o’clock

This is very natural in Finnish. Time expressions often come early in the sentence.

No. You could also say:

• Pyykkivuoro on huomenna kello kahdeksalta.

That means the same thing. The difference is mostly about emphasis:

• Huomenna... = focuses first on tomorrow
• Pyykkivuoro... = focuses first on the laundry slot

Because kahdeksalta means at eight o’clock.

In Finnish, when you say the time when something happens, you usually use this form:

• yhdeltä = at one
• kahdelta = at two
• kolmelta = at three
• kahdeksalta = at eight

So:

• kello kahdeksalta = at eight o’clock

Just kahdeksan by itself is simply eight, not at eight.

Yes, kello can often be omitted.

• Pyykkivuoro on kello kahdeksalta.
• Pyykkivuoro on kahdeksalta.

Both are natural. Kello makes it extra clear that you are talking about a clock time.

Kahdeksalta has the ending -lta/-ltä, which is the ablative ending in Finnish. In time expressions, this ending is commonly used to mean at a certain clock time.

So learners often just memorize this pattern as:

• at one = yhdeltä
• at two = kahdelta
• at eight = kahdeksalta

It is one of those very common Finnish time patterns that is best learned through examples.

Joten means so, therefore, or thus. It introduces a result.

• Pyykkivuoro on kello kahdeksalta, joten herään aikaisin. = The laundry slot is at eight, so I wake up early.

By contrast, koska means because and introduces a reason.

Compare:

• Herään aikaisin, koska pyykkivuoro on kello kahdeksalta.
  = I wake up early because the laundry slot is at eight.

So:

• joten = result
• koska = reason

Because joten joins two clauses, and in Finnish that normally takes a comma.

The two parts are:

• Huomenna pyykkivuoro on kello kahdeksalta
• joten herään aikaisin

So the comma helps separate the first idea from the result that follows.

Herään is the first person singular present tense of herätä = to wake up.

So:

• herään = I wake up / I will wake up

The ending -n tells you the subject is I, which is why minä does not have to be stated.

Because Finnish usually does not have a separate future tense. The present tense is often used for future events when the context makes the time clear.

Here, Huomenna already tells us this is about the future:

• Huomenna ... herään aikaisin. = Tomorrow ... I’ll wake up early.

So in Finnish, present tense + a future time word often does the job of English future tense.

Because the verb ending already shows the subject.

• herään = I wake up
• heräät = you wake up
• herää = he/she/it wakes up

Since -n already means I, Finnish often leaves out minä unless you want extra emphasis or contrast.

So:

• Herään aikaisin. = normal
• Minä herään aikaisin. = more emphatic, like I wake up early

Because aikaisin is an adverb, while aikainen is an adjective.

Here you need an adverb because it describes how I wake up:

• herään aikaisin = I wake up early

Compare:

• aikainen aamu = an early morning
  here aikainen describes a noun, so it is an adjective

Most likely a one-time future event, or at least a specific planned event. Even though Finnish uses the present tense, the word Huomenna makes it clear that this refers to tomorrow.

So the sense is:

• Tomorrow my laundry slot is at eight, so I’ll wake up early.

That is a very normal way to express future plans in Finnish.