É importante que você comece a revisar o relatório agora.

Because é importante que... typically triggers the present subjunctive in Portuguese. The subjunctive is used after expressions of importance, necessity, doubt, etc., because they present something as recommended/desired rather than just stating a fact.

• Indicative (fact): Você começa a revisar agora. = You start reviewing now.
• Subjunctive (recommendation/importance): É importante que você comece... = It’s important that you start...

The verb is começar (to start). In the present subjunctive, it becomes:

• que eu comece
• que você comece
• que ele/ela comece
  ...
  So que você comece is the correct form. Notice the spelling change (ç → c) because ce already gives the soft s sound that ç would indicate.

Yes, that’s also common in Brazilian Portuguese. It uses the infinitive (começar) instead of the subjunctive clause.

• É importante que você comece... = a bit more formal / explicit clause
• É importante você começar... = very common, slightly more direct

Both are natural.

Portuguese uses ser (é) for general statements/assessments of something as a concept: It is important (as a general evaluation). Estar would sound unusual here because estar is more about temporary states/conditions, and importante in this structure is typically framed as a general judgment: É importante...

Começar a + infinitive is the most common way to say to start doing something in Portuguese. So:

• começar a revisar = to start reviewing
  You may also hear começar a revisar much more than alternatives like começar revisando in everyday speech.

Not normally. After começar, Portuguese generally uses a + infinitive: começar a fazer / começar a revisar. Without a, it sounds incomplete or ungrammatical in standard usage.

In Brazil, você is very common for you in most everyday situations. Even though it means you, it takes third-person singular verb forms:

• você comece, você começa, você começou, etc.
  If you used tu, you’d typically get tu comeces (in places where tu is used with full agreement).

It’s fairly flexible, but the meaning/emphasis can shift slightly. Natural options include:

• ...agora. (neutral, common)
• ...agora mesmo. (stronger: right now)
• É importante que você comece agora a revisar o relatório. (focuses “now” a bit more)

The original placement (...o relatório agora) is very natural.

Portuguese often uses the definite article (o/a/os/as) more than English does, especially when referring to a specific known item: the report.
You can drop the article in some contexts (especially headings, notes, or very generic mentions), but in a normal sentence like this, o relatório is the standard choice.

All are possible, with slightly different flavor:

• revisar = review (very standard for documents)
• rever = review again / re-check (can imply going over something)
• checar = check (more casual; sometimes closer to “verify”)
  For a report/document, revisar o relatório is a very natural default.

It’s neutral and common, but it can feel a bit “businesslike.” More casual options include:

• É bom você começar a revisar o relatório agora. (It’d be good for you to start...)
• Melhor você começar a revisar o relatório agora. (You’d better start...)
• Você precisa começar a revisar o relatório agora. (You need to start...)