Ten formularz jest krótki, ale mój wniosek musi być dokładny.

Because formularz is a masculine singular noun in the nominative case.

In Polish, the demonstrative this changes to match the noun’s gender:

• ten for masculine nouns
• ta for feminine nouns
• to for neuter nouns

So:

• ten formularz = this form

If the noun were feminine, you would use ta. If it were neuter, you would use to.

For the same reason: wniosek is also a masculine singular noun in the nominative case, so the possessive adjective has to agree with it.

Polish my changes like this:

• mój for masculine singular
• moja for feminine singular
• moje for neuter singular and some plural uses

So:

• mój wniosek = my application / my request

Both adjectives are in the same form: masculine singular nominative. The difference is just due to normal Polish spelling and adjective patterns.

A very useful rule:

• many masculine adjectives end in -y
• but after certain consonants, especially k and g, Polish often uses -i instead

So:

• krótki ends in -i because of the k
• dokładny takes the more typical -y

Both mean the adjective is agreeing with a masculine singular noun.

Because they are predicate adjectives after być (to be), and in Polish, predicate adjectives normally stay in the nominative.

So:

• Formularz jest krótki
• Wniosek musi być dokładny

That is different from many predicate nouns, which often appear in the instrumental:

• On jest lekarzem = He is a doctor

So a helpful contrast is:

• adjective after być → usually nominative
• noun after być → often instrumental

Because musi is a modal verb meaning must, and modal verbs in Polish are followed by an infinitive.

Here the infinitive is być = to be.

So the structure is:

• musi być dokładny = must be accurate / must be exact

You cannot normally say:

• musi dokładny

That would be incomplete, because musi needs the verb być here.

They express two different ideas:

• jest = is
  This states a fact.
• musi być = must be
  This states necessity or requirement.

So:

• Ten formularz jest krótki = this form is short
• ale mój wniosek musi być dokładny = but my application must be exact / accurate

Even though both parts involve being, the second part adds the idea of obligation.

In normal standard Polish, no.

You generally need jest in a sentence like this:

• Ten formularz jest krótki

Leaving it out:

• Ten formularz krótki

sounds unnatural in ordinary speech and writing. You might see omission in:

• headlines
• notes
• poetry
• very informal shorthand

But for normal learners, it is best to keep jest.

Wniosek is a very useful Polish word because it can mean different things depending on context, such as:

• application
• request
• petition
• motion
• conclusion / inference

In a bureaucratic or official context, wniosek often means something like:

• an application
• a formal request

So in this sentence, it most likely refers to an official application or request, not a logical conclusion.

Ale is the normal word for a clear but.

It shows a stronger contrast:

• the form is short
• but the application must be exact

Polish a can also link two clauses, but it often feels softer, more like:

• and
• while
• whereas
• sometimes a mild but

So in this sentence, ale is the most natural choice because the contrast is strong and clear.

Because Polish has no articles.

English needs words like:

• a
• an
• the

Polish does not. Whether something is definite or indefinite usually comes from:

• context
• word order
• extra words like ten (this)

So:

• formularz can mean a form or the form
• ten formularz makes it more specific: this form

Yes, Polish word order is more flexible than English word order.

This sentence has a very natural, neutral order:

• Ten formularz jest krótki, ale mój wniosek musi być dokładny.

You can change the order for emphasis, but the meaning stays similar if the forms are clear. For example, moving words around can make one part sound more contrastive or more formal.

Still, for learners, this version is a very good default because it sounds natural and straightforward.

Yes, you could say just wniosek if the context already makes it clear whose application it is.

But mój is included to emphasize:

• it is my application
• the contrast is specifically between this form and my application

So the sentence becomes more personal and more precise.

A rough learner-friendly guide:

• ten ≈ ten
• formularz ≈ for-MOO-larsh
• jest ≈ yest
• krótki ≈ KROOT-kee
• ale ≈ AH-leh
• mój ≈ mooy
• wniosek ≈ VNYO-sek
• musi ≈ MOO-shee
• być ≈ difficult to match exactly in English, but roughly bihch with a shorter vowel
• dokładny ≈ do-KWAD-nih

A few key pronunciation points:

• j sounds like English y
• w sounds like English v
• sz sounds like sh
• ó sounds like u
• ć is a soft consonant with no perfect English equivalent

It can mean several related things, depending on context:

• exact
• accurate
• precise
• thorough
• detailed

In this sentence, dokładny suggests that the application must be prepared carefully and precisely. So depending on context, a very natural English translation could be:

• exact
• accurate
• precise
• thorough

That is normal in Polish: one adjective can cover a range of closely related meanings.