Mój brat mieszka obok.

Because mój has to agree with brat.

Here:

• brat = masculine singular
• it is the subject of the sentence
• so it is in the nominative case

That means the possessive adjective mój also appears in its masculine singular nominative form: mój.

A few related forms are:

• moja siostra = my sister
• moje dziecko = my child
• moi bracia = my brothers

So mój brat is the correct matching form.

Brat is in the nominative case.

It is the subject of the sentence—the person who lives—so Polish uses the nominative.

The basic dictionary form is:

• brat = brother

In this sentence, that form stays unchanged because it is the subject:

• Mój brat mieszka obok.

Mieszka is the 3rd person singular present tense form of the verb mieszkać.

So the conjugation goes like this:

• ja mieszkam = I live
• ty mieszkasz = you live
• on/ona/ono mieszka = he/she/it lives
• my mieszkamy = we live
• wy mieszkacie = you live
• oni/one mieszkają = they live

Since brat = he, the sentence uses mieszka.

Usually yes, but specifically in the sense of reside / live somewhere.

So mieszkać is used for where someone lives:

• Mieszkam w Warszawie. = I live in Warsaw.
• Ona mieszka sama. = She lives alone.

It is not the main verb for to be alive or to live life in a broad philosophical sense. For those ideas, Polish often uses other verbs, especially żyć.

So in this sentence, mieszka clearly means lives/resides.

Here obok means something like:

• nearby
• next door
• close by
• beside

The exact English translation depends on context.

Used on its own, obok often means nearby / next door:

• Mój brat mieszka obok. = My brother lives nearby / next door.

But obok can also be used with a noun, in which case it means next to / beside:

• obok domu = next to the house
• obok szkoły = beside the school

So obok can work both:

1. independently, as in this sentence
2. with a noun phrase, usually followed by the genitive

Polish often does not need an extra word if obok already gives the idea of location.

So:

• Mój brat mieszka obok.

is perfectly natural and complete.

Adding something else is only necessary if you want more precision:

• Mój brat mieszka tutaj obok. = My brother lives right nearby here.
• Mój brat mieszka obok mnie. = My brother lives next to me / nearby me.

In short, obok by itself can already function as the location expression.

Yes. When obok is followed by a noun, that noun is usually in the genitive case.

Examples:

• obok domu = next to the house
• obok sklepu = next to the shop
• obok mnie = next to me

So you can compare:

• Mój brat mieszka obok.
  = My brother lives nearby / next door.

• Mój brat mieszka obok szkoły.
  = My brother lives next to the school.

Grammatically, yes. But the meaning changes slightly.

• Mój brat mieszka obok. = My brother lives nearby.
• Brat mieszka obok. = A/The brother lives nearby, depending on context

Without mój, Polish no longer explicitly says whose brother it is. In real conversation, that may still be clear from context, but mój brat is the normal form if you want to say my brother.

Yes. Polish word order is more flexible than English, although the basic sentence:

• Mój brat mieszka obok.

is the most neutral.

Other possible orders include:

• Obok mieszka mój brat.
• Mieszka obok mój brat.

These alternatives may sound more marked or may shift the focus:

• Obok mieszka mój brat. can emphasize nearby/next door
• Mój brat at the start is neutral and straightforward

So the original sentence is a very natural default order.

A rough pronunciation guide is:

• mój ≈ mooy
• brat ≈ braht
• mieszka ≈ MYESH-kah
• obok ≈ OH-bok

A few helpful details:

• ó is pronounced like u
• sz sounds like sh
• mie in mieszka starts with a soft mye sound

So a rough full version is:

mooy braht MYESH-kah OH-bok

Yes: Polish often uses possessive words like mój, moja, moi with family nouns quite naturally:

• mój brat = my brother
• moja mama = my mom
• mój ojciec = my father

However, in some contexts Polish can omit the possessive if it is obvious:

• Brat przyjedzie jutro. = My/The brother will come tomorrow.

Still, if you are introducing or clearly identifying the person, mój brat is very normal and natural.

It can mean either, depending on context.

Obok is somewhat broad. It can suggest:

• next door
• right nearby
• beside

If you want to be more precise, Polish can say:

• Mój brat mieszka obok mnie. = My brother lives next to me.
• Mój brat mieszka w sąsiedztwie. = My brother lives nearby / in the neighborhood.
• Mój brat mieszka drzwi obok. = My brother lives next door. (more colloquial/contextual)

So the original sentence is natural but a little context-dependent in exact English wording.