Mój brat i jego żona dobrze się rozumieją.

Because brat is a masculine singular noun, and mój must agree with it.

• mój = my (for masculine singular nouns)
• moja = my (for feminine singular nouns)
• moje = my (for neuter singular nouns)

So:

• mój brat = my brother
• moja siostra = my sister
• moje dziecko = my child

In this sentence, brat is masculine, so mój is the correct form.

They are both in the nominative case, because together they form the subject of the sentence.

• mój brat = my brother
• jego żona = his wife

Since the sentence is about what they do, both nouns stay in nominative:

• Mój brat i jego żona = My brother and his wife

Even though there are two nouns, each one is singular on its own; together they make a plural subject.

Here jego means his.

So:

• jego żona = his wife

A useful thing to know is that jego does not change to match the gender of the noun after it in this possessive use. That is different from mój / moja / moje, which do change.

For example:

• jego brat = his brother
• jego żona = his wife
• jego dziecko = his child

So jego stays the same.

That is a very common question.

Swój usually refers back to the subject of the clause, especially when someone owns something connected to themselves:

• Mój brat kocha swoją żonę. = My brother loves his own wife.

But in Mój brat i jego żona..., the phrase jego żona is part of the subject itself. It is identifying which woman we mean: his wife.

So jego żona is the natural choice here.

Using swój in this exact structure would not sound natural in standard Polish.

Here się makes the verb reciprocal: it shows that the two people understand each other.

So:

• rozumieć = to understand
• rozumieć się = to understand each other / to get along well

That means:

• Mój brat i jego żona dobrze się rozumieją
  = My brother and his wife understand each other well / get along well

Without się, the meaning changes.

They are related, but not the same.

• rozumieć = to understand
• rozumieć się = to understand each other, to get along, to be on the same wavelength

Examples:

• Rozumiem ten tekst. = I understand this text.
• Oni się rozumieją. = They understand each other.

So in your sentence, rozumieją się is not just plain understand. It has the idea of a mutual relationship between the two people.

Rozumieją is the 3rd person plural present tense form of rozumieć.

The basic verb is:

• rozumieć = to understand

Present tense forms include:

• rozumiem = I understand
• rozumiesz = you understand
• rozumie = he/she/it understands
• rozumiemy = we understand
• rozumiecie = you (plural) understand
• rozumieją = they understand

Because the subject is my brother and his wife = they, Polish uses rozumieją.

Because the subject has two people:

• mój brat
• jego żona

Joined by i (and), they form a plural subject, so the verb must also be plural:

• rozumieją = they understand

A useful extra note: in the present tense, Polish uses the same 3rd person plural verb form here regardless of whether the group is all male, all female, or mixed. So you simply use rozumieją.

Dobrze is an adverb, and here it means well.

So:

• dobrze się rozumieją = understand each other well / get along well

It describes how they understand each other.

Compare:

• dobry = good (adjective)
• dobrze = well (adverb)

Examples:

• To jest dobry film. = This is a good film.
• On dobrze mówi po polsku. = He speaks Polish well.

Not completely. Polish word order is fairly flexible, although some versions sound more neutral than others.

The given sentence:

• Mój brat i jego żona dobrze się rozumieją.

is a very natural, neutral way to say it.

You could also hear:

• Mój brat i jego żona rozumieją się dobrze.

This is also correct, but the emphasis shifts slightly.

So the basic meaning stays the same, but word order can affect style, rhythm, or emphasis.

Yes, you can, although it is often unnecessary.

For example:

• Mój brat i jego żona dobrze się ze sobą rozumieją.

This is more explicit: with each other.

But in most cases, się already makes the mutual meaning clear, so:

• Mój brat i jego żona dobrze się rozumieją.

is perfectly natural on its own.

It can mean both, depending on context.

Dobrze się rozumieją can suggest:

• they understand each other well
• they communicate well
• they get along well
• they are on the same wavelength

So it often carries a slightly broader, more relationship-based meaning than a literal English understand.

That is why this expression is very common when talking about couples, friends, coworkers, or family members.