Não te preocupes com isso agora.

Because preocupar-se is a pronominal/reflexive verb in Portuguese when it means to worry.

So the basic pattern is:

• preocupar-se = to worry
• preocupar-te = to worry yourself
• preocupar-me = to worry myself

In this sentence, te shows that the speaker is talking to you in the tu form:

• Não te preocupes = Don’t worry

English does not usually use a reflexive pronoun here, but Portuguese does.

Because this is a negative command: Don’t worry.

In European Portuguese, negative commands use the present subjunctive, not the normal present indicative.

Compare:

• Tu preocupas-te. = You worry / you are worrying.
• Não te preocupes. = Don’t worry.

So preocupes is not random: it is the correct subjunctive/negative imperative form for tu.

Yes — in meaning, it is a negative imperative or negative command/request.

Portuguese grammars often explain it like this:

• affirmative command for tu: uses the imperative form
  
  • Preocupa-te.
• negative command for tu: uses the present subjunctive
  
  • Não te preocupes.

So it functions as Don’t worry, even though the verb form comes from the subjunctive.

Because não triggers proclisis, which means the object/reflexive pronoun goes before the verb.

So:

• Preocupa-te. = affirmative command
• Não te preocupes. = negative command

After não, European Portuguese normally places the clitic pronoun before the verb. So não preocupes-te would be incorrect.

Portuguese often omits subject pronouns when they are clear from the verb form.

In preocupes, the ending -es shows that the sentence is addressing tu.

So:

• Não te preocupes com isso agora.
• Tu não te preocupes com isso agora.

Both are possible, but the version without tu is more natural in most situations.

Because the verb expression is preocupar-se com something.

So the pattern is:

• preocupar-se com alguma coisa = to worry about something

Examples:

• Preocupo-me com o exame. = I worry about the exam.
• Não te preocupes com isso. = Don’t worry about that.

The preposition com is simply part of the structure this verb normally uses.

This is about Portuguese demonstratives.

Very roughly:

• isto = this, near the speaker / something being introduced
• isso = that, near the listener / something already mentioned
• aquilo = that over there, farther away from both

In a sentence like Não te preocupes com isso agora, isso is very natural because it usually refers to that matter / that thing we already know about.

So if someone has just mentioned a problem, the response Não te preocupes com isso agora means Don’t worry about that now.

It is informal singular, because it uses the tu form:

• Não te preocupes... = informal, to one person you call tu

More formal versions would be different, for example:

• Não se preocupe com isso agora. = formal singular
• Não se preocupem com isso agora. = plural (vocês)

So this sentence is the kind of thing you would say to a friend, family member, child, partner, etc., depending on your relationship and the region.

A Brazilian learner or speaker would usually expect something like:

• Não se preocupe com isso agora.

That is because Brazilian Portuguese often uses você rather than tu, and with você the verb goes in the third person singular.

So:

• European Portuguese informal: Não te preocupes com isso agora.
• Brazilian Portuguese common version: Não se preocupe com isso agora.

In some parts of Brazil, tu is used, but the most widely recognized neutral Brazilian version is não se preocupe.

Yes. Portuguese allows some flexibility in word order for emphasis.

These are all possible:

• Não te preocupes com isso agora.
• Agora não te preocupes com isso.
• Com isso, não te preocupes agora. (more marked / more literary or context-dependent)

The original sentence is very natural and neutral.
If you move agora to the front, you emphasize now a bit more:

• Agora não te preocupes com isso. = For now, don’t worry about that.

Usually it sounds reassuring or comforting, not rude.

It often means something like:

• Don’t worry about that now.
• Try not to think about that right now.
• Leave that for later.

Of course, tone matters. Said gently, it is comforting. Said impatiently, it could sound dismissive. But grammatically, the sentence itself is perfectly normal and often kind in tone.