Learn Hardcore Finnish: Huoltomies korjaa kahvinkeitintä keittiössä. - The maintenance man is repairing the coffee maker in the kitchen.

Finnish has no articles at all, so there is no direct equivalent of English a/an or the.
Definiteness or indefiniteness is understood from context.
So huoltomies can mean a maintenance man or the maintenance man, depending on what the speaker has in mind and what has already been mentioned.

What are the dictionary (basic) forms of the words in the sentence?

Huoltomies → basic form: huoltomies (“maintenance man”)
korjaa → basic form: korjata (“to repair, to fix”)
kahvinkeitintä → basic form: kahvinkeitin (“coffee maker”)
keittiössä → basic form: keittiö (“kitchen”)

What tense is korjaa, and does it mean “fixes” or “is fixing”?

Korjaa is the 3rd person singular present tense of korjata.
Finnish does not have a separate continuous/progressive tense, so korjaa can mean both:

“(he) fixes / repairs” (general or repeated action)
“(he) is fixing / is repairing (right now)” (current, ongoing action)
Context usually tells which is meant.

Why is it kahvinkeitintä and not just kahvinkeitin or kahvinkeittimen?

Kahvinkeitintä is in the partitive singular case.
Finnish often uses the partitive object when:

the action is ongoing, incomplete, or unbounded, or
the amount is not seen as a whole.

So Huoltomies korjaa kahvinkeitintä suggests that the fixing is in progress, not yet completed.

If you said Huoltomies korjaa kahvinkeittimen, with a total object (genitive/accusative), it would focus more on the completion of fixing “the whole coffee maker” (e.g. as a planned or completed event).

What exactly does the ending -tä in kahvinkeitintä mean?

The ending -ta / -tä marks the partitive singular.
Here, kahvinkeitin (coffee maker) + -tä → kahvinkeitintä.

So grammatically:

kahvinkeitin = a/the coffee maker (basic form)
kahvinkeitintä = “(some) coffee maker” as a partitive object, chosen because the repairing is seen as ongoing or not yet completed.

What is the structure of the word kahvinkeitin?

Kahvinkeitin is a compound:

kahvin = genitive of kahvi (“coffee”) → “coffee’s”
keitin = “boiler / cooker / maker”

So literally it’s “coffee’s boiler/maker” = coffee maker.
When you inflect it, the ending is added to the whole compound: kahvinkeitin → kahvinkeitintä, kahvinkeittimen, etc.

Why is kahvinkeitintä spelled with -tä, not -ta?

The choice between -ta and -tä follows vowel harmony.
The “harmony class” of kahvinkeitin is determined mainly by its last element keitin, which historically belongs to the front-vowel class (connected to keittää, with ä).

Because of that, it takes the front variant -tä:

keitin → keitintä
compound: kahvinkeitin → kahvinkeitintä

What case is keittiössä, and what does the ending -ssä mean?

Keittiössä is in the inessive case, marked by -ssa / -ssä, which usually means “in”.

So:

keittiö = kitchen
keittiössä = “in the kitchen”

Because keittiö has the front vowel ö, it takes the front-harmony ending -ssä rather than -ssa.

How would the meaning change if we used keittiöön or keittiöstä instead of keittiössä?

These are all local cases with different meanings:

keittiössä = in the kitchen (inessive: inside, location)
keittiöön = into the kitchen (illative: movement into)
keittiöstä = out of / from the kitchen (elative: movement out of)

So the original sentence describes where the fixing is happening (in the kitchen), not movement to or from the kitchen.

Is the word order “Huoltomies korjaa kahvinkeitintä keittiössä” fixed, or can it be changed?

Finnish word order is relatively flexible.
The given order (Subject–Verb–Object–Place) is neutral and common:

Huoltomies korjaa kahvinkeitintä keittiössä.

You can change the order mainly for emphasis or focus, e.g.:

Keittiössä huoltomies korjaa kahvinkeitintä.
→ Emphasis on in the kitchen (not somewhere else).
Kahvinkeitintä huoltomies korjaa keittiössä.
→ Emphasis on the coffee maker (perhaps as opposed to some other device).

The basic meaning (who fixes what where) stays the same.

Is huoltomies gendered, and is there a more gender-neutral option?

Yes. Huoltomies literally means “maintenance man” (mies = man), so it is male-gendered.
More gender-neutral alternatives include:

huoltaja (carer / maintenance person, depending on context)
huoltotyöntekijä (“maintenance worker”)

In many real-life contexts, people still say huoltomies, but neutral terms are used more and more.

How would the sentence change if the subject were plural, “The maintenance men are fixing the coffee maker in the kitchen”?

You would pluralize the subject and conjugate the verb in the plural:

Huoltomiehet korjaavat kahvinkeitintä keittiössä.

Changes:

huoltomies → huoltomiehet (plural subject)
korjaa → korjaavat (3rd person plural)
The object kahvinkeitintä and location keittiössä stay the same.

How would you say that the fixing is completed, like “The maintenance man fixed the coffee maker in the kitchen”?

You’d use past tense and a total object:

Huoltomies korjasi kahvinkeittimen keittiössä.

Changes:

korjaa (present) → korjasi (past)
kahvinkeitintä (partitive: ongoing/incomplete) → kahvinkeittimen (genitive/total object: whole item, completed event)

This sentence presents the fixing as a finished event.