Po pracy mój płaszcz jest brudny od błota.

Because po in the meaning after requires the locative case in Polish.

• Dictionary form: praca = work
• Locative singular: pracy

So:

• po pracy = after work

This is a very common pattern:

• po szkole = after school
• po obiedzie = after dinner
• po spotkaniu = after the meeting

Even though pracy looks like other case forms too, here it is specifically the form used after po.

Usually it means after work in a general sense, just like in English.

So:

• Po pracy = after work / after finishing work

It does not usually mean one specific piece of work. If you wanted to say after the job/task, the context would need to make that clearer.

Mój means my, so mój płaszcz = my coat.

In Polish, possessives are often used when you want to be clear or emphasize ownership. Sometimes Polish can omit possessives when the meaning is obvious from context, especially with body parts or very familiar situations, but here mój płaszcz sounds normal and natural.

So:

• mój płaszcz = my coat

It agrees with płaszcz, which is:

• masculine
• singular
• nominative here

That is why the form is mój.

Because brudny has to agree with płaszcz.

Płaszcz is:

• masculine
• singular

So the adjective must also be masculine singular:

• brudny = dirty

Compare:

• płaszcz jest brudny = the coat is dirty
• koszula jest brudna = the shirt is dirty
• okno jest brudne = the window is dirty

The adjective changes depending on the gender of the noun.

In the present tense, Polish normally does use jest in sentences like this.

So:

• Mój płaszcz jest brudny. = My coat is dirty.

You generally should not omit jest here in normal standard Polish.

That is different from Russian, for example, where the present-tense to be is often omitted. In Polish, jest is normally expressed.

Brudny od błota is the natural Polish way to say that something is dirty because of mud or with mud on it.

Here od suggests the source or cause of the dirtiness:

• brudny od błota = dirty from mud / muddy

Using z here would sound unnatural in this meaning.

Other similar examples:

• mokry od deszczu = wet from the rain
• lepki od soku = sticky from juice
• brudny od farby = dirty with paint / stained by paint

So this is a phrase pattern worth learning:
adjective + od + genitive.

Because od requires the genitive case.

• Dictionary form: błoto = mud
• Genitive singular: błota

So:

• od błota = from mud / because of mud

This is a very common case pattern in Polish:

• od deszczu = from the rain
• od kurzu = from dust
• od śniegu = from snow

Not exactly.

• brudny od błota means dirty with mud or covered/spattered with mud
• błotnisty means muddy, but it is more often used for things like:
  • błotnista droga = a muddy road
  • błotnisty teren = muddy ground

For clothing, brudny od błota sounds very natural. For terrain or surfaces, błotnisty is often more likely.

Polish word order is flexible, and putting Po pracy first sets the time frame right away:

• Po pracy mój płaszcz jest brudny od błota.
• Literally: After work, my coat is dirty with mud.

This sounds natural because Polish often places time expressions at the beginning.

You could also say:

• Mój płaszcz jest po pracy brudny od błota.

But that is less natural here. The original version is smoother and more typical.

Yes. That is often the most natural English translation.

Literally, Polish says:

• my coat is dirty from mud

But natural English would often be:

• After work, my coat is muddy.
• After work, my coat is dirty with mud.
• After work, my coat is covered in mud.
  depending on context

So the Polish structure and the most idiomatic English wording do not have to match exactly.

It is in the nominative case, because it is the subject of the sentence.

• mój = my
• płaszcz = coat

Together:

• mój płaszcz = my coat

This is the thing being described as dirty, so it stays in the basic subject form.

It can do either, depending on context.

It may mean:

• After work today, my coat is dirty with mud
  or
• After work, my coat ends up dirty with mud as a repeated situation

Polish often leaves that distinction to context, just as English does with after work.

Yes, it is natural and correct.

A native speaker would understand it easily. Depending on style and context, they might also say something like:

• Po pracy mój płaszcz jest cały w błocie. = After work, my coat is covered in mud.
• Po pracy mój płaszcz jest ubrudzony błotem. = After work, my coat is dirtied with mud.

But Po pracy mój płaszcz jest brudny od błota is perfectly good Polish.