Do tej półki potrzebna jest długa śruba, nie krótki gwóźdź.

Here do does not express movement. With the genitive case, do can also mean something like for, for use with, or suitable for.

So do tej półki means for this shelf.

This kind of use is common in Polish. For example:

• klucz do drzwi = a key for the door / to the door
• farba do ścian = paint for walls

So in this sentence, do tej półki tells you what the screw is needed for.

Because do requires the genitive case.

The basic dictionary form is:

• ta półka = this shelf

After do, both words change to genitive singular:

• ta → tej
• półka → półki

So:

• ta półka = this shelf
• do tej półki = for this shelf

Because potrzebny works like an adjective and must agree with the thing that is needed.

The needed item here is długa śruba. Since śruba is a feminine singular noun, the adjective must also be feminine singular:

• potrzebny jest gwóźdź = a nail is needed
• potrzebna jest śruba = a screw is needed
• potrzebne są śruby = screws are needed

So potrzebna is chosen because of śruba.

Polish word order is more flexible than English word order.

Potrzebna jest długa śruba is a very natural pattern and means literally something like needed is a long screw. In normal English we would not say it that way, but in Polish it sounds fine.

You could also rearrange the sentence, for example:

• Długa śruba jest potrzebna do tej półki

That means the same basic thing, but the emphasis changes slightly. Polish often moves words around to highlight different parts of the sentence.

Because it is the thing being identified as needed in the structure potrzebna jest X.

In this pattern, the noun phrase after jest is normally in the nominative:

• potrzebna jest śruba
• potrzebny jest gwóźdź

So długa śruba stays in nominative singular.

Because this is really a shortened second clause.

The full idea is something like:

• Do tej półki potrzebna jest długa śruba, nie jest potrzebny krótki gwóźdź.

The second jest potrzebny is left out because it is understood from the first part.

Since gwóźdź is also the thing being named as needed or not needed, it stays in the nominative:

• krótki gwóźdź

So the contrast is:

• długa śruba
• nie krótki gwóźdź

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

Here:

• śruba is feminine → długa śruba
• gwóźdź is masculine → krótki gwóźdź

So the adjective endings are different because the nouns have different grammatical genders.

Usually yes in a broad everyday sense, but there is a small nuance.

• śruba often means screw or bolt in general
• gwóźdź means nail

In more technical Polish, a wood screw is often called wkręt, but in everyday usage learners will often see śruba used broadly. For the purpose of this sentence, the important contrast is simply:

• śruba = screw-type fastener
• gwóźdź = nail

Yes. A natural alternative would be:

Do tej półki trzeba długiej śruby, nie krótkiego gwoździa.

That means almost the same thing, but the grammar changes:

• potrzebna jest długa śruba → nominative
• trzeba długiej śruby → genitive

So both patterns are useful to learn, but they do not take the same case.

The comma marks a clear contrast: one thing is correct, the other is not.

The sentence sets up an opposition:

• długa śruba
• nie krótki gwóźdź

In English, we might also pause there:

• a long screw, not a short nail

So the comma helps separate the two contrasted noun phrases.

Yes. Polish allows several natural word orders, depending on emphasis. For example:

• Do tej półki potrzebna jest długa śruba, nie krótki gwóźdź.
• Długa śruba jest potrzebna do tej półki, nie krótki gwóźdź.
• Do tej półki nie krótki gwóźdź jest potrzebny, tylko długa śruba.

These all express roughly the same idea, but they highlight different parts of the message. The original version is natural and puts the context for this shelf first.