Learn Hardcore Russian: Проект уже закончен, и я доволен. - The project is already finished, and I am satisfied.

In Russian, the present-tense verb быть (to be) is normally omitted: Проект (есть) закончен. Using есть here would sound emphatic or книжно (bookish) and is uncommon in everyday speech. The meaning is finished is carried by the predicate form закончен.

What exactly is закончен grammatically?

Закончен is a short-form passive participle (краткое страдательное причастие) from the perfective verb закончить (to finish). Short-form participles are commonly used as predicates to describe a resulting state: The project is finished (as a result).

Why is it закончен (masculine) and not some other ending?

It agrees with проект, which is masculine singular nominative.

проект (masc.) → закончен
feminine: работа закончена
neuter: письмо закончено
plural: дела закончены

What’s the difference between закончен and законченный?

закончен (short form) is typically predicate-only: Проект закончен = The project is finished (statement of status/result).
законченный (full form) behaves like a regular adjective and often modifies a noun: законченный проект = a finished/complete project.
You can also say Проект законченный, but that’s less neutral and often sounds like you’re classifying it as a finished-type project, not simply stating completion.

Does уже have to be placed where it is?

Уже (already) is flexible but has preferred positions.

Neutral: Проект уже закончен.
Also possible: Проект закончен уже. (often more conversational, sometimes slightly emphatic like it’s finished already)
Less common/marked: Уже проект закончен. (can work in specific contexts but feels more stylistic)

Why is there a comma before и?

Because и connects two independent clauses with their own subjects/predicates: 1) Проект уже закончен
2) я доволен
So the comma is standard: ..., и ....
Without the comma, it would tend to read like a single clause with shared structure, which isn’t the case here.

What is доволен—an adjective? Why is it not довольный?

Доволен is the short-form adjective of довольный (satisfied/pleased). Russian often uses short-form adjectives as predicates to express a current state:

Я доволен. = I’m satisfied. Full form довольный is more typical as an attributive adjective: довольный человек (a satisfied person), though Я довольный is possible but sounds more descriptive/characterizing and less like a simple state.

Do I need to say what I’m satisfied with (like with the project)?

Not necessarily. Я доволен can stand alone if the context is clear.
If you want to specify, Russian usually uses the instrumental case:

Я доволен проектом. = I’m satisfied with the project. You can also specify with a clause: Я доволен, что проект закончен. = I’m glad/satisfied that the project is finished.

Can the subject я be omitted here?

Usually you keep it: ..., и я доволен.
Omitting it (..., и доволен.) can happen in very informal speech when the subject is obvious, but it can sound incomplete or stylistically clipped. In writing, и я доволен is the safe, standard choice.

Is there any aspect nuance behind закончен?

Yes. Закончен comes from perfective закончить, which focuses on the completed result: the project reached its endpoint. If you wanted to describe the process (was being finished), you’d use an imperfective construction instead, e.g. Проект заканчивали / Проект заканчивался depending on meaning.

Are there common alternative words for закончен in this sentence?

Yes, with slightly different tone:

Проект уже завершён (a bit more formal; completed)
Проект уже готов (means ready, not necessarily emphasizing the act of finishing)
Проект уже окончен (similar to закончен, can sound a bit more formal/bookish)

What are the stress patterns I should know here?

Common standard stresses:

проЕкт (stress on е)
закОнчен (stress on о)
довОлен (stress on the second о)