Learn Hardcore Finnish: Kun neuvottelu päättyy, valmistamme ja allekirjoitamme sopimuksen vastaanotossa. - When the negotiation ends, we prepare and sign the agreement at the reception.

Kun means when/once and introduces a temporal clause for an event viewed as certain to happen. Jos means if and introduces a conditional clause for something hypothetical or uncertain. Since the speaker knows the negotiation will end, Kun is the correct choice.

Why is neuvottelu singular instead of neuvottelut, when in English we often say “negotiations”?

In Finnish neuvottelu (singular) can refer to the negotiation process as a whole, much like a mass noun. You use singular when you think of it as one continuous event. Plural neuvottelut would emphasize multiple rounds or distinct negotiations. Both are grammatically correct, but singular is common for a single negotiation.

Why is there a comma after Kun neuvottelu päättyy?

In Finnish, a subordinate clause (here a temporal clause starting with Kun) is separated by a comma when it comes before the main clause. So you write:
Kun neuvottelu päättyy, valmistamme …

What does päättyy mean, and why is it in the third person singular present tense?

The verb päättyä means to end/come to an end. It’s conjugated for neuvottelu (a singular noun) in present tense, third person:
neuvottelu + päättyy = the negotiation ends.

How do you form valmistamme and allekirjoitamme, and why isn’t there an explicit pronoun like “we”?

Finnish verbs include the subject in their endings, so pronouns are often omitted. For 1st person plural present tense you take the stem and add -mme:

valmista- → valmistamme (“we prepare”)
allekirjoitta- → allekirjoitamme (“we sign”)

Why is the object sopimus in the form sopimuksen (-n ending) instead of the partitive sopimusta?

The ending -n here marks the accusative (total object), used when the action affects the entire object and is completed:
valmistamme ja allekirjoitamme sopimuksen = “we prepare and sign the whole contract.”
The partitive sopimusta would imply an incomplete action or just part of it.

What does vastaanotossa mean, and why is it in the inessive case (-ssa)?

Vastaanotossa = “in/at the reception area.” Finnish uses cases instead of prepositions. The inessive case -ssa/ssä expresses location in something. So:
vastaanotto + ssa → vastaanotossa = “at/in the reception.”

Could you swap the clauses to say Valmistamme ja allekirjoitamme sopimuksen vastaanotossa, kun neuvottelu päättyy?

Yes. Finnish word order is quite flexible. Moving the subordinate clause to the end is perfectly acceptable. Just keep the comma before kun. The meaning stays the same.

What’s the nuance between päättyä and loppua, since both can mean “to end”?

päättyä is used for formal processes, events or meetings ending (e.g. negotiations, a ceremony).
loppua is more general: something comes to an end or runs out (e.g. time, supplies, a movie).
Here the formal tone of päättyä fits a negotiation.

How do you pronounce allekirjoitamme, especially since it’s quite long?

Finnish always stresses the first syllable. You break it down as:
AL-le-kir-joi-tam-me

Double consonants like kk are held slightly longer.
Each vowel or diphthong is pronounced clearly.