Learn Hardcore Finnish: Illalla tiskaan astiat, koska astianpesukone on täynnä. - In the evening I wash the dishes because the dishwasher is full.

Finnish often drops subject pronouns because the verb ending already shows the person. tiskaan is the 1st person singular form (I wash/do the dishes), so minä is optional and usually only added for emphasis or contrast.

What does Illalla mean grammatically, and why is it in that form?

Illalla is a time expression meaning in the evening. It’s in the adessive case (-lla/-llä), which is commonly used for “at/on” times:

aamulla = in the morning
päivällä = during the day
illalla = in the evening

What tense is tiskaan, and how is it formed?

tiskaan is present tense. The verb is tiskata (to do the dishes / to wash dishes).
Conjugation (present, singular) looks like:

(minä) tiskaan = I do the dishes
(sinä) tiskaat = you do the dishes
(hän) tiskaa = he/she does the dishes

In Finnish, the present tense can also cover near-future plans depending on context (like “I’ll do it this evening”).

Why is astiat in this form? What case is it?

astiat is the plural of astia (dish/container) and here it’s in the plural nominative form. With many common actions (including tiskata), the object is often expressed as a total object, especially when you mean you’ll wash all the dishes (the whole set).

Could the object be astioita instead of astiat? What would that change?

Yes. astioita is the partitive plural. The difference is usually:

tiskaan astiat = I’ll wash the dishes (all of them / the whole batch)
tiskaan astioita = I’ll wash some dishes / dishes in general (not necessarily all)

So astiat suggests completeness; astioita suggests an indefinite or partial amount.

Why does Finnish use koska here, and does it affect word order?

koska means because and introduces a subordinate clause. Finnish word order is fairly flexible, but in a koska-clause you typically keep a normal statement order: subject + verb + complement:
astianpesukone on täynnä = dishwasher is full

Also, Finnish commonly uses a comma before koska when it introduces a reason clause like this.

What exactly is astianpesukone? Why is it such a long word?

astianpesukone means dishwasher and it’s a compound word:

astian = of a dish (genitive of astia)
pesu = washing
kone = machine

So literally: dish-washing-machine. Finnish builds many everyday nouns this way.

Why is it astianpesukone (singular) and not something plural?

Because it refers to one dishwasher. The sentence is: the dishwasher is full. If you meant multiple dishwashers (unusual in everyday context), you’d use astianpesukoneet (plural).

What does on täynnä mean, and why not just a single word like “full”?

Finnish often expresses “to be full” as olla täynnä:

on = is (3rd person singular of olla)
täynnä = full

täynnä is a word that typically goes with olla to describe a state (similar to an adjective/predicate). You can think of olla täynnä as one common expression meaning to be full.

Is täynnä an adjective? Does it change form?

It behaves like a predicate describing a state, but it doesn’t inflect like a normal adjective in the same way (you don’t usually make it agree in number/case like iso/isoa/isot, etc.). You typically use it in this fixed-looking form with olla:

Kuppi on täynnä. = The cup is full.
Huone on täynnä ihmisiä. = The room is full of people.

Why is there a comma before koska?

In Finnish, a subordinate clause introduced by koska is usually separated with a comma from the main clause:
Illalla tiskaan astiat, koska astianpesukone on täynnä.
This is standard written punctuation.

Could the clauses be reversed: Koska astianpesukone on täynnä, illalla tiskaan astiat?

Yes, that’s grammatically fine. If the koska-clause comes first, you still use a comma after it. The meaning stays basically the same, but the emphasis shifts slightly to the reason first:
Koska astianpesukone on täynnä, illalla tiskaan astiat.