Bez drenażu roślina ani nie rośnie, ani się nie ukorzenia.

Because bez always requires the genitive case in Polish.

The dictionary form is drenaż. After bez, it changes to drenażu:

• drenaż = nominative
• bez drenażu = genitive after bez

This is a very common pattern:

• bez cukru = without sugar
• bez wody = without water
• bez problemu = without a problem

So after bez, you should automatically expect the next noun to be in the genitive.

Because roślina is the subject of the sentence, so it stays in the nominative.

Only the noun after bez changes case. The phrase bez drenażu is just an adverbial phrase meaning without drainage; it does not control the form of roślina.

So the structure is basically:

• Bez drenażu = prepositional phrase
• roślina = subject
• ani nie rośnie, ani się nie ukorzenia = predicate

Ani... ani... is the standard Polish way to say neither... nor....

So:

• ani nie rośnie, ani się nie ukorzenia
  means
• neither grows nor takes root

It links two negative parts in a balanced way. This construction is very common in Polish.

Because in Polish this is the normal grammar of negative concord.

In English, learners are often taught to avoid double negatives, but Polish works differently. In Polish, when a clause is negative, the verb normally also stays negative.

So this pattern is correct:

• ani nie rośnie, ani się nie ukorzenia

Not using nie here would sound wrong in standard Polish.

It comes from the infinitive rosnąć = to grow.

Its present-tense forms are not fully transparent from the infinitive, so you mostly have to learn them as a set:

• rosnę = I grow
• rośniesz = you grow
• rośnie = it grows

Here the subject is singular (roślina), so Polish uses 3rd person singular: rośnie.

Also, Polish present tense can cover both:

• grows
• is growing

The exact nuance depends on context.

It means something like takes root or becomes rooted.

The verb is ukorzeniać się / ukorzenić się. In this sentence, the form is imperfective present:

• ukorzenia się

The important thing is that się belongs to the verb. It is not optional here.

Compare:

• ukorzeniać się = to take root
• ukorzeniać = to root something / to cause something to root

So with a plant as the subject, się is needed because the plant itself is undergoing the process.

Because się is fairly mobile in Polish.

Both of these are possible:

• się nie ukorzenia
• nie ukorzenia się

In this sentence, ani się nie ukorzenia sounds natural because się often appears early in its clause and often avoids standing at the very end.

So the key thing to learn is this: the position of się is flexible, and Polish word order is generally freer than English word order.

Because the sentence states a general truth or general rule.

It is not about one specific moment only; it means that without drainage, this is what happens in general. Polish commonly uses the imperfective present for that:

• nie rośnie
• nie ukorzenia się

Using a perfective form would suggest a completed future event instead. For example:

• ukorzeni się = it will take root

That would not fit as well here.

Yes, people would understand you, but it is less balanced than the original.

The version with repeated ani:

• ani nie rośnie, ani się nie ukorzenia

is the clearest and most idiomatic equivalent of neither... nor.... It has a nice parallel structure and sounds more polished.

So:

• nie rośnie ani się nie ukorzenia = understandable
• ani nie rośnie, ani się nie ukorzenia = more elegant and standard in this kind of sentence

The comma is there because of the repeated paired structure:

• ani..., ani...

Polish normally separates the two coordinated parts with a comma in this kind of construction.

But Bez drenażu is just a short opening phrase. Short introductory prepositional phrases like that usually do not need a comma.

So the punctuation reflects the structure:

• no comma after the short opener
• comma between the two ani parts