Learn Hardcore Finnish: Lompakko on takin taskussa. - The wallet is in the coat pocket.

On is the 3rd person singular form of the verb olla (to be). The subject lompakko (wallet) is singular, so you use on.
Plural would be Lompakot ovat ... (The wallets are ...).

What case is takin, and what does it do here?

Takin is genitive singular of takki (coat). The genitive often marks possession or “belonging to”:
takin tasku = the coat’s pocket / a pocket of the coat.
So takin taskussa literally means in the coat’s pocket.

What case is taskussa, and why is it used?

Taskussa is inessive singular of tasku (pocket). The inessive case ending -ssa/-ssä means in (inside something).
So taskussa = in the pocket.

Why is the ending -ssa (not -ssä)?

Finnish uses vowel harmony:

If a word has back vowels (a, o, u), it typically takes -ssa.
If it has front vowels (ä, ö, y), it takes -ssä.

Tasku contains u (a back vowel), so it takes -ssa → taskussa.

Why does takki become takin (where did one k go)?

That’s consonant gradation, a common Finnish sound/letter change when adding certain endings.
takki (strong grade kk) → takin (weak grade k) in the genitive singular.

Does this sentence mean the wallet / a wallet? Where is the article?

Finnish has no articles (a/an/the). Lompakko can be interpreted as the wallet or a wallet depending on context.
Often, in a practical situation, English would use the: The wallet is in the coat pocket.

Is takin taskussa more like “in the coat pocket” or “in a pocket of the coat”?

Both readings are possible, and context decides. Grammatically it’s in the coat’s pocket (genitive + noun + inessive). In English you often say in the coat pocket or in a pocket of the coat.

Can I change the word order?

Yes. Finnish word order is flexible and changes emphasis. For example:

Lompakko on takin taskussa. (neutral)
Takin taskussa on lompakko. (emphasizes location; also like “There is a wallet in the coat pocket.”)
Lompakko on taskussa. (only “in the pocket”; context must tell whose/which pocket)

How would I say in my coat pocket?

Common options:
1) Using a possessive suffix on takki: Lompakko on takkini taskussa. (in my coat’s pocket)
2) Using minun (often more emphatic): Lompakko on minun takin taskussa.
In everyday Finnish, option 1 is often preferred.

Could Finnish also express this as one word, like a compound?

Yes, compounds are common. You may see:
Lompakko on takkitaskussa. = in the coat pocket
Here takkitasku (coat pocket) is a compound noun, and takkitaskussa is its inessive form.

What’s the difference between saying taskussa vs something like taskulle or taskusta?

They are different location/direction cases:

taskussa (inessive) = in the pocket (location)
taskuun (illative) = into the pocket (movement in)
taskusta (elative) = out of the pocket (movement out)
taskulla (adessive) = on/at the pocket (less natural here unless a different meaning is intended)

How is Lompakko on takin taskussa pronounced (roughly)?

A rough guide (not perfect English spelling, but helpful):

Lompakko ≈ LOM-pak-koh (double kk is held longer)
on ≈ on (short)
takin ≈ TAH-kin
taskussa ≈ TAHS-koo-sah (the ss is long)
Length matters in Finnish: double consonants (like kk, ss) are pronounced longer than single ones.