La projekto estos finita post unu monato.

La is the definite article, like the in English.

So la projekto means the project, not just a project. It suggests that the speaker and listener already know which project is being talked about.

A few useful comparisons:

• la projekto = the project
• projekto = a project or project in a general sense

Esperanto has no separate word for a/an.

Estos is the future-tense form of esti, which means to be.

The ending -os marks the future tense in Esperanto.

So:

• estas = is / are / am
• estis = was / were
• estos = will be

That means estos by itself means will be.

This is a very common Esperanto pattern:

• esti
  • participle

Here:

• estos = will be
• finita = finished

Together, estos finita means will be finished.

This construction is useful when you want to focus on the result or state of something, rather than on who does the action.

So the sentence is about the condition of the project after a certain time: it will be in a finished state.

This is about the meaning of the participle.

• finita = finished, completed
• finata = being finished, in the process of being finished

So:

• estos finita = will be finished
• estos finata = will be being finished or will still be in the process of being finished

In your sentence, the idea is that after one month, the project will already be complete. That is why finita is the right form.

Because participles in Esperanto behave like adjectives.

The ending -a is the adjective ending, and finita agrees with projekto.

So:

• projekto = singular
• finita = singular adjective/participle describing it

If the noun were plural, the participle would also be plural:

• La projektoj estos finitaj. = The projects will be finished.

Because projekto is the subject of the sentence, not the direct object.

In Esperanto, the -n ending marks the direct object. But here, the sentence is passive:

• La projekto estos finita = The project will be finished

The project is the thing receiving the action, but in a passive sentence it becomes the grammatical subject.

Compare:

• Active: Iu finos la projekton. = Someone will finish the project.
• Passive: La projekto estos finita. = The project will be finished.

In the active version, projekton gets -n because it is the direct object. In the passive version, projekto does not.

Literally, it means after one month.

In natural English, this is often translated as in one month, depending on context.

The idea is: when one month has passed, the project will be finished.

A useful nuance:

• post unu monato = after one month has passed
• ene de unu monato = within one month

So if you want to emphasize a deadline no later than one month, ene de unu monato may be better. But for the sentence you gave, post unu monato is perfectly normal.

Because monato comes after the preposition post.

Normally, after a preposition like post, the noun does not take -n.

So:

• post unu monato = after one month

You may have seen time expressions with -n, such as:

• Mi atendis unu monaton. = I waited one month.

That is different: there is no preposition there. In your sentence, post already shows the relationship, so monato stays without -n.

Yes. Esperanto word order is fairly flexible.

You can say:

• La projekto estos finita post unu monato.
• Post unu monato la projekto estos finita.

Both are correct. The difference is mostly emphasis:

• starting with La projekto focuses first on the project
• starting with Post unu monato focuses first on the time

Both are natural.

Yes, you could, and it would also be natural.

There is a small difference in nuance:

• La projekto estos finita = the project will be in a finished state
• La projekto finiĝos = the project will come to an end / get finished

In many everyday situations, the two are very close in meaning. But estos finita is a more explicitly passive/result-focused form, while finiĝos uses a single verb and feels a bit more like will get finished or will end.