Quando avremo finito di montare tutto, inviteremo il vicinato a bere un tè nel salone.

Because the sentence is talking about a future moment, and the finishing will be completed before the inviting happens.

Avremo finito is the future perfect:

• avremo = future of avere
• finito = past participle of finire

So it literally means we will have finished.

Italian often uses future forms after time words like quando, appena, and dopo che when the meaning is future. English usually does not do this in the same way.

• Italian: Quando avremo finito..., inviteremo...
• English: When we have finished..., we will invite...

Because the whole situation is in the future.

• avremo finito = we will have finished
• inviteremo = we will invite

The first action will be completed first, and then the second action will happen. So Italian uses:

• future perfect for the earlier completed action
• simple future for the later action

This is a very common pattern in Italian.

After finire, Italian normally uses di + infinitive when you mean to finish doing something.

So:

• finire di montare = to finish assembling
• abbiamo finito di mangiare = we finished eating
• ha finito di leggere = he/she finished reading

So avremo finito di montare tutto means we will have finished assembling everything.

Here montare means to assemble, to put together, or to set up.

This verb is often used for things like:

• furniture
• shelves
• equipment
• anything that comes in pieces and has to be assembled

So in this sentence, it probably suggests they are putting together furniture or setting up a room or house.

Because tutto is the direct object of montare: it means everything.

So:

• montare tutto = to assemble everything

This word order is completely normal in Italian. The infinitive comes first, and the object follows it.

Compare:

• mangiare tutto = to eat everything
• comprare tutto = to buy everything
• sistemare tutto = to arrange everything

Not exactly.

Il vicinato is a collective noun. It means something like:

• the neighborhood
• the local neighbors as a group
• the people living nearby

I vicini means the neighbors more directly, as individual people.

So:

• inviteremo i vicini = we will invite the neighbors
• inviteremo il vicinato = we will invite the neighborhood / the local community around us

In this sentence, il vicinato sounds a little broader and more collective.

Because Italian commonly uses the pattern:

invitare qualcuno a fare qualcosa
= to invite someone to do something

So:

• invitare il vicinato a bere un tè = to invite the neighbors to have tea
• invitare gli amici a cena = to invite friends for dinner
• invitare qualcuno a entrare = to invite someone to come in

Here, a bere literally means to drink, but in natural English the whole phrase is often better translated as to have tea.

Because Italian often uses the indefinite article in expressions like this when referring to a serving or a cup of something.

So:

• bere un tè = to have a tea / to have some tea
• bere un caffè = to have a coffee
• prendere una birra = to have a beer

In English, a tea can sound less natural in some contexts, so translation may become to have tea. But the Italian un tè is perfectly normal.

Nel is the contraction of:

in + il = nel

So:

• nel salone = in the salone

Salone usually means a large living room, main sitting room, or big reception room. Depending on context, it can be translated as:

• living room
• main room
• lounge
• sometimes hall or salon

So nel salone tells you where they plan to serve the tea.

Because the auxiliary verb here is avere, and with avere the past participle usually does not agree with the subject.

So:

• avremo finito = we will have finished

Even though we refers to more than one person, finito stays in its default form.

You would usually see agreement with essere, not with avere:

• siamo andati
• siamo finite (if all speakers are feminine)

With avere, agreement only happens in some more specific cases, especially with a preceding direct object pronoun.

Yes, you could, but the nuance is slightly different.

• Quando finiremo di montare tutto = when we finish assembling everything
• Quando avremo finito di montare tutto = when we will have finished assembling everything

In many contexts, both are possible. But avremo finito emphasizes the idea of completed result more clearly: first everything will be assembled, and only then will they invite the neighborhood.

So the original version sounds especially natural if the speaker wants to stress completion before the next step.