Zdrowe korzenie ani nie usychają, ani nie gniją.

It is the standard Polish pattern for neither ... nor .... It links two negative parts of the sentence:

• ani nie usychają
• ani nie gniją

You can think of it as the negative counterpart of i ... i ... = both ... and ....

Because in Polish, the verbs themselves stay negated. So ani nie usychają, ani nie gniją is the normal structure.

This is standard Polish, not a mistake. Polish often uses multiple negative elements in one sentence, for example:

• Nikt nic nie wie = Nobody knows anything

A useful comparison:

• when ani... ani... joins full verb phrases, each verb is usually negated
• when it joins subjects, you often get one nie with the main verb, for example Ani Jan, ani Maria nie przyszli

It is the nominative plural form of korzeń = root.

Here it is the subject of the sentence, so nominative is the expected case.

• singular: korzeń
• plural: korzenie

Because the adjective must agree with the noun in number, gender, and case.

Korzenie is plural, but it does not refer to male persons, so it takes the non-masculine-personal plural adjective form zdrowe.

Compare:

• zdrowe korzenie = healthy roots
• zdrowi mężczyźni = healthy men

So zdrowi is for masculine-personal groups, not for things like roots.

Because the subject korzenie is plural.

In Polish, the verb agrees with the subject in person and number, so a plural subject takes plural verb forms. Both verbs here are 3rd person plural present tense:

• usychają = they wither / dry up
• gniją = they rot

Their basic forms are:

• usychać = to wither, dry up gradually
• gnić = to rot, decay

The sentence uses their present-tense plural forms:

• usychać → usychają
• gnić → gniją

Because Polish present tense, especially with imperfective verbs, can describe:

• something happening now
• a repeated process
• a general truth

Here the sentence sounds like a general statement about healthy roots, so the present tense is natural.

Not if you want the same meaning.

Forms like uschną and zgniją are perfective, so they usually refer to a completed result in the future: will dry up, will rot.

This sentence is not talking about a future completed event. It is saying what healthy roots do not do in general, so the imperfective forms nie usychają and nie gniją are the better choice.

Because that is the normal, neutral order in Polish for an adjective modifying a noun:

• zdrowe korzenie

That is the straightforward equivalent of healthy roots. Putting the adjective after the noun is possible in some contexts, but it is usually more marked or stylistic.

Because in Polish, repeated conjunctions like ani ... ani ... normally take a comma before the second part.

So this is standard punctuation:

• ani nie usychają, ani nie gniją

You will see the same kind of comma with other repeated pairings too.

A rough English-style guide is:

• Zdrowe → ZDRO-veh
• korzenie → ko-ZHE-nye
• ani nie → AH-nyi nyeh
• usychają → u-sy-HA-yon
• gniją → GNYEE-yon

A few useful sound notes:

• rz sounds like the s in measure
• ni before a vowel often sounds like ny
• final ą is nasal, so it is not a plain English o sound