Обжалование началось сегодня.

Обжалование is a verbal noun: a noun made from a verb. It comes from обжаловать, meaning to appeal or challenge a decision in a legal or official sense.

So in this sentence, обжалование names the action/process itself, not the person doing it. This is common in formal Russian, especially legal or bureaucratic language.

Because началось must agree with the subject обжалование.

• обжалование is neuter
• it is singular
• so the past tense form is началось

Compare:

• процесс начался — the process began
• жалоба началась — this would be grammatically feminine, though semantically odd
• обжалование началось — correct for this sentence

The key point is that Russian past tense agrees in gender and number with the subject.

Because the sentence means that the beginning already happened earlier today.

Russian uses the past tense here exactly as English does in a sentence like:

• The appeal began today

So сегодня does not force the present tense. It just tells you when the event happened.

This is an aspect question.

• началось is perfective
• начиналось is imperfective

Here, Russian uses perfective because it reports a completed event: the moment of beginning took place.

So Обжалование началось сегодня means:

• the start happened today

If you used начиналось, it would sound more like:

• it was beginning
• it used to begin
• it began repeatedly
• or it is background description in a larger story

Without special context, началось is the normal choice.

Here сегодня is an adverb meaning today.

It answers the question when?

• Началось когда? — Сегодня

It is not functioning as a noun with a case ending here, so you do not need to think of it as nominative, accusative, and so on in this sentence.

Yes. Russian word order is flexible.

These are all possible:

• Обжалование началось сегодня. — neutral
• Сегодня началось обжалование. — emphasizes today
• Обжалование сегодня началось. — can sound a bit more contrastive, as if today is being highlighted against some other time

The basic meaning stays the same, but the emphasis changes.

Not exactly.

• жалоба = a complaint, grievance, or sometimes the actual appeal document
• обжалование = the act or process of appealing/challenging something

So:

• подать жалобу = to file a complaint/appeal
• обжалование решения = the appeal/challenge of a decision

In your sentence, обжалование sounds more like an official process than a single document.

You usually add it after обжалование, often in the genitive:

• Обжалование решения началось сегодня. — The appeal of the decision began today.
• Обжалование приговора началось сегодня. — The appeal of the verdict began today.
• Обжалование отказа началось сегодня. — The appeal of the refusal began today.

So the pattern is often:

обжалование + genitive noun

Yes, very much so.

Обжалование началось сегодня sounds official, legal, administrative, or news-like. In everyday conversation, people might prefer a more concrete or simpler wording, depending on the situation, for example:

• Сегодня подали апелляцию.
• Сегодня начали обжаловать решение.

So the original sentence is natural, but it belongs to a more formal register.

Yes. A very common alternative is to use a personal or impersonal verb construction, for example:

• Сегодня начали обжаловать решение. — Today they started appealing the decision.
• Решение начали обжаловать сегодня. — The decision began to be appealed today.

Compared with these, Обжалование началось сегодня sounds more abstract and official, because it turns the action into a noun.