Po pracy nauka polskiego jest dla mnie trudna.

Because po in the sense of after takes the locative case in Polish.

The noun praca changes to pracy in the locative singular:

• praca = work
• po pracy = after work

So this is a case-governed form, not a random spelling change.

Yes, nauka can mean science, but it can also mean learning or study.

Here, in nauka polskiego, it clearly means learning/studying. Context tells you which meaning is intended.

So:

• nauka = learning / study
• in other contexts, nauka can also = science

Because nauka normally takes the genitive case for the thing being learned.

So:

• nauka czego? = learning of what?
• polskiego = of Polish

This is very similar to how some English nouns use of, as in the study of Polish.

Also, polskiego here is basically Polish language in a shortened form. A fuller version would be nauka języka polskiego.

Grammatically, it is an adjective form, but it is being used like a noun.

Polish often does this with language names:

• uczę się polskiego = I am learning Polish
• lubię angielski = I like English

So in this sentence, polskiego means the Polish language, even though the form itself is adjectival.

The subject is nauka polskiego.

That whole phrase means learning Polish and functions as the thing being described. The sentence is saying that this subject is trudna.

The other parts are not the subject:

• po pracy = time expression
• dla mnie = for me

Because trudna has to agree with nauka, which is a feminine singular noun.

In Polish, adjectives match the noun they describe in gender, number, and usually case.

So:

• nauka is feminine
• therefore trudna must also be feminine

If the subject were different, the adjective would change:

• kurs jest trudny = the course is difficult
• zadanie jest trudne = the task is difficult

Dla mnie means for me and shows whose perspective we are talking about.

The preposition dla takes the genitive case, so ja becomes mnie:

• dla
  • genitive
• mnie = genitive form of ja

So jest dla mnie trudna means is difficult for me.

Not directly in this exact structure.

With this sentence pattern, dla mnie is the natural choice:

• Nauka polskiego jest dla mnie trudna.

If you want to use mi, Polish usually switches to a different structure:

• Po pracy trudno mi uczyć się polskiego.

Both sentences are natural, but they are built differently:

• jest dla mnie trudna = noun-based structure
• trudno mi uczyć się = impersonal structure with mi

Yes, in normal standard Polish, jest is needed.

Polish does not normally drop the present-tense form of to be in ordinary sentences like this. So:

• Nauka polskiego jest dla mnie trudna = correct
• Nauka polskiego dla mnie trudna = not standard as a normal sentence

You might see omission only in very informal notes, headlines, or poetic style.

Yes. Polish word order is fairly flexible, because the case endings show the grammatical relationships.

For example, these are all possible:

• Po pracy nauka polskiego jest dla mnie trudna.
• Nauka polskiego po pracy jest dla mnie trudna.
• Dla mnie nauka polskiego po pracy jest trudna.

They all mean roughly the same thing, but the emphasis changes a little. Starting with Po pracy highlights the time frame first.

This sentence is correct and natural, but many speakers might also say:

Po pracy trudno mi uczyć się polskiego.

That version can sound a bit more conversational because it focuses on the action to learn rather than the noun learning.

So:

• Po pracy nauka polskiego jest dla mnie trudna. = correct, a bit more noun-based
• Po pracy trudno mi uczyć się polskiego. = also correct, often more conversational