A rede elétrica do bairro está com problema.

A is the feminine singular definite article, meaning the.

It is used because rede is a feminine singular noun:

• a rede = the network
• a rede elétrica = the electrical grid / power network

Portuguese usually uses definite articles more often than English, so A rede elétrica sounds natural where English says The electrical grid.

Literally, rede elétrica means electrical network.

In everyday Brazilian Portuguese, it commonly refers to:

• the power grid
• the electricity network
• the local electrical supply system

So in this sentence, it means the neighborhood’s electrical system or power grid, not just a single wire or cable.

In Portuguese, adjectives usually come after the noun.

So:

• rede elétrica = electrical network
• literally: network electrical

That is the normal word order. Putting elétrica before rede would sound unnatural here.

Also, some noun + adjective combinations become very standard expressions, and rede elétrica is one of them.

Because do is a contraction:

• de + o = do

So:

• do bairro = of the neighborhood

This kind of contraction is extremely common in Portuguese:

• de + a = da
• de + os = dos
• de + as = das

So a rede elétrica do bairro literally means the electrical grid of the neighborhood.

Yes, functionally it does.

Portuguese often expresses possession or association with de:

• a rede elétrica do bairro = the neighborhood’s electrical grid
• literally: the electrical grid of the neighborhood

English often prefers the ’s form, but Portuguese usually uses de + article/noun instead.

Estar com problema is a very common way in Brazilian Portuguese to say that something is having a problem, is experiencing trouble, or is malfunctioning.

So:

• está com problema = is having a problem / is in trouble

This structure suggests a current condition or temporary issue.

You may also hear:

• tem problema = has a problem
• está com um problema = is having a problem
• apresenta problema = more formal, presents/shows a problem

In everyday speech, está com problema sounds very natural.

Portuguese has two main verbs for to be:

• ser for more permanent or essential characteristics
• estar for temporary states or conditions

Here, the power grid is not being described as inherently defective forever. It is in a temporary problematic state right now.

So:

• A rede elétrica do bairro está com problema = it currently has a problem

Using é com problema would be incorrect here.

In Portuguese, after com, a noun often appears without an article when the speaker is talking in a general way.

So:

• está com problema = is having trouble / has a problem
• está com um problema = is having a problem with a bit more emphasis on one specific problem

Both are possible, but está com problema is very common and idiomatic in everyday Brazilian Portuguese.

Problema is masculine: o problema.

This is one of several Portuguese words of Greek origin that end in -ma but are masculine:

• o problema
• o sistema
• o tema
• o programa

So if you include an article, you would say:

• um problema
• o problema

not uma problema or a problema.

Yes.

There is a small nuance:

• está com problema = is having trouble / has a problem; often a general statement
• está com problemas = is having problems; may suggest multiple issues or a more serious situation

In casual speech, both can work. The singular is very common even when the exact number of issues is not important.

Está is the third-person singular present indicative of estar.

It agrees with a rede elétrica, which is singular:

• eu estou
• você/ele/ela está
• nós estamos
• eles/elas estão

So está means is here.

Not with the same meaning.

• do bairro = of the neighborhood / the neighborhood’s
• no bairro = in the neighborhood

Compare:

• A rede elétrica do bairro está com problema.
  = The neighborhood’s electrical grid has a problem.

• A rede elétrica no bairro está com problema.
  = The electrical grid in the neighborhood has a problem.

The second one is possible, but it shifts the meaning slightly from ownership/association to location.

It is understandable and fairly natural, but in everyday Brazilian Portuguese people might often say things like:

• A rede elétrica do bairro está com problema.
• A rede elétrica do bairro está com algum problema.
• A energia do bairro está com problema.
• A luz do bairro está com problema.
• A rede elétrica do bairro está com defeito.

In casual speech, many Brazilians would more often refer to a energia or a luz, depending on context. But your original sentence is perfectly reasonable, especially when talking specifically about the electrical grid/system.