A professora pediu para eu terminar o trabalho da escola hoje.

Here pediu para means asked someone to do something.

• pedir = to ask, to request, or to ask for
• pedir para + infinitive is a very common Brazilian Portuguese pattern

So A professora pediu para eu terminar... means The teacher asked me to finish...

Because pedir and perguntar are used for different kinds of ask in Portuguese.

• perguntar = to ask a question
• pedir = to ask/request that something be done

In this sentence, the teacher is not asking a question. She is making a request, so pediu is the right verb.

Portuguese normally uses the definite article with common nouns like professora when talking about a specific person.

So A professora simply means the teacher.

This is very natural in Portuguese. English also says the teacher, so this part matches English fairly well.

In standard Portuguese, eu is used here because it is the subject of the infinitive terminar.

A useful rule is:

• mim cannot be the subject of a verb
• eu can be the subject of a verb

In para eu terminar, eu is the one who will terminar.

You may hear pra mim terminar in everyday speech in Brazil, but it is generally considered nonstandard. The standard form is para eu terminar.

Yes. That is also very natural.

A professora me pediu para terminar... explicitly includes me as the person who was asked.

The original sentence, A professora pediu para eu terminar..., is also correct. It identifies the person through eu, the subject of terminar.

In everyday Brazilian Portuguese, both patterns are common, but these are especially natural:

• A professora pediu para eu terminar...
• A professora me pediu para terminar...

Using both me and eu together is possible, but it can sound heavier than necessary.

Because after pedir para, Portuguese commonly uses the infinitive.

So:

• pediu para eu terminar = very common, especially in speech
• pediu que eu terminasse = also correct, but more formal or more structured

The sentence could also be:

A professora pediu que eu terminasse o trabalho da escola hoje.

That version uses the subjunctive, but the original sentence is more everyday Brazilian Portuguese.

Usually it means something like:

• the school assignment
• the school project
• the schoolwork

The exact meaning depends on context.

In school contexts, trabalho often means an assignment or project, not just work in a general sense. So a native English speaker will often translate trabalho da escola more naturally as school assignment or school project.

Because da is a contraction of:

• de + a = da

Portuguese very often contracts prepositions with articles.

So:

• de a escola becomes da escola

Literally, trabalho da escola is work of the school, but in natural English it usually means school assignment, work for school, or schoolwork, depending on context.

In the most natural reading, hoje goes with terminar:

The teacher asked me to finish the school assignment today.

So the likely idea is that the finishing should happen today.

However, depending on context, someone could also understand it as the teacher asked me today. If you want to make that meaning clearer, Portuguese would often put hoje earlier:

Hoje, a professora pediu para eu terminar o trabalho da escola.

Yes, Portuguese allows some flexibility, and changing the order can change the emphasis.

For example:

• Hoje, a professora pediu para eu terminar o trabalho da escola.
  Emphasizes today as the time when she asked.

• A professora pediu para eu terminar hoje o trabalho da escola.
  Emphasizes today as the time when I should finish it.

• A professora pediu para eu terminar o trabalho da escola hoje.
  Very natural, neutral everyday order.

So the original sentence is completely normal.

Yes. In Brazilian Portuguese, para is very often pronounced pra in everyday speech.

So you will commonly hear:

A professora pediu pra eu terminar o trabalho da escola hoje.

That is extremely natural in conversation. In more formal writing, para is usually preferred.

Yes. A more formal version would be:

A professora pediu que eu terminasse o trabalho da escola hoje.

This uses que + subjunctive instead of para + infinitive.

Both are correct, but:

• pediu para eu terminar = more common in everyday Brazilian Portuguese
• pediu que eu terminasse = more formal, more written-style, or more careful speech