O para-brisa e o limpador de para-brisa têm problemas.

Because Portuguese often repeats the article when two specific nouns are joined by e.

So:

• o para-brisa = the windshield
• o limpador de para-brisa = the windshield wiper

Repeating o makes it clear that these are two separate items. In this sentence, that is the most natural choice.

Para-brisa means windshield in Brazilian Portuguese.

It is a compound word, historically built from the idea of something that stops/breaks the breeze/wind. Portuguese keeps a hyphen in this word.

A useful spelling note:

• Modern spelling: para-brisa
• Older spelling: pára-brisa

After the spelling reform, the accent in pára disappeared, but the hyphen stayed.

Because limpador de para-brisa is the normal fixed expression for windshield wiper.

Here, de works like for/of in a naming sense:

• limpador de para-brisa = windshield wiper / wiper for the windshield

If you say limpador do para-brisa, it sounds more literal, like the cleaner/wiper of the windshield of a specific car. That can be grammatical, but it is less like a dictionary-style name for the object.

So in general:

• limpador de para-brisa = standard name of the part
• limpador do para-brisa = more situational, tied to a specific windshield

Because the subject is plural.

The subject is:

• O para-brisa e o limpador de para-brisa
  = The windshield and the windshield wiper

Two things joined by e usually take a plural verb, so:

• ele tem = he/it has
• eles têm = they have

That is why the sentence uses têm.

The accent helps distinguish the singular and plural forms of ter in writing:

• ele/ela tem = he/she/it has
• eles/elas têm = they have

So the circumflex in têm marks the third-person plural form.

A useful extra note: in many Brazilian accents, tem and têm can sound very similar in everyday speech, but the spelling difference is still required.

Because each noun refers to one item, but together they form a plural subject.

So:

• o para-brisa = one windshield
• o limpador de para-brisa = one windshield wiper

When you combine them with e, the whole subject becomes plural:

• the windshield and the wiper → have

So the nouns stay singular, but the verb becomes plural.

It is problemas because the sentence says they have problems in the plural.

Also, problema is one of the Portuguese nouns that ends in -a but is still masculine.

So:

• o problema = the problem
• os problemas = the problems

This happens with several words of Greek origin, such as:

• o sistema
• o tema
• o problema

So the sentence correctly uses:

• têm problemas

The most useful forms are:

• o para-brisa → os para-brisas
• o limpador de para-brisa → os limpadores de para-brisa

Notice:

1. para-brisa by itself commonly becomes para-brisas
2. In limpador de para-brisa, the main noun is limpador, so that is the part that normally changes in the plural

So:

• the windshields = os para-brisas
• the windshield wipers = os limpadores de para-brisa

Yes. Grammatically, the singular form refers to one windshield wiper.

If you want to be clearly plural, you would say:

• os limpadores de para-brisa

In real-life usage, context matters. Sometimes people speak loosely about the wiper system, but in straightforward grammar:

• singular: o limpador de para-brisa
• plural: os limpadores de para-brisa

Têm problemas is natural and correct. It means have problems in a general sense.

Brazilian Portuguese also often uses estar com for this kind of idea:

• O para-brisa e o limpador de para-brisa estão com problemas.
• O para-brisa e o limpador de para-brisa estão com problema.

These are also very common in everyday speech, especially when talking about things that are malfunctioning.

So both patterns are useful:

• ter problemas = more direct, very standard
• estar com problema(s) = very common in conversation

A rough pronunciation guide is:

oo pah-rah-BREE-zah ee oo leem-pah-DOR jee pah-rah-BREE-zah TENG pro-BLAY-mahs

A few helpful notes:

• o often sounds like oo
• brisa sounds like BREE-zah
• limpador has stress on -dor
• de may sound like jee in many Brazilian accents
• têm is often pronounced very similarly to tem in Brazil, even though the spelling is different

This is only an approximation, but it is a useful starting point.