Na dobry posiłek potrzeba kilku prostych składników: ryżu, warzyw i trochę oleju.

Here na means for. With the accusative, na can express purpose or intended use.

So na dobry posiłek means something like for a good meal or to make a good meal.

Similar examples:

• na obiad = for lunch
• na prezent = as a present / for a present
• na kolację = for dinner

Because na in this meaning takes the accusative.

The noun posiłek is masculine inanimate, and for masculine inanimate nouns, the accusative singular is the same as the nominative singular:

• nominative: dobry posiłek
• accusative: dobry posiłek

So after na, dobry posiłek is the correct form here.

In this sentence, potrzeba is an impersonal expression meaning there is a need for, one needs, or it takes.

So:

• potrzeba kilku prostych składników = several simple ingredients are needed
• more literally: there is a need for several simple ingredients

This is related to potrzebować (to need), but the grammar is different.

Compare:

• Potrzebuję ryżu. = I need rice.
• Potrzeba ryżu. = Rice is needed.

Because potrzeba is followed by the genitive.

That makes the whole phrase genitive plural:

• kilka → kilku
• proste → prostych
• składniki → składników

So kilku prostych składników means of several simple ingredients in form, even though in natural English we would just say several simple ingredients.

Kilka is the basic form, but here the sentence needs the genitive, so it changes to kilku.

A simple way to think of it:

• kilka składników = nominative/accusative-style form
• kilku składników = genitive form

Since potrzeba requires genitive, kilku is the right choice.

Because the colon introduces a list of examples of składników, and those examples stay in the same case required by the sentence.

In other words, the sentence is really saying:

• kilku prostych składników: ryżu, warzyw i trochę oleju

Since składników is genitive, the listed items are also given in genitive:

• ryż → ryżu
• warzywa → warzyw
• olej → oleju

This is very normal in Polish.

Because ryż and olej are usually treated as mass nouns: you normally mean some rice and some oil, not separate countable items.

So Polish uses:

• ryżu = genitive singular
• oleju = genitive singular

But warzywa is commonly used as a plural category meaning vegetables, so here you get:

• warzyw = genitive plural

So the grammar reflects how these foods are normally talked about.

Trochę means a little, a bit of, or some.

It is a quantity word, and it normally requires the following noun to be in the genitive:

• trochę oleju = a little oil
• trochę wody = a little water
• trochę czasu = a little time / some time

So oleju is genitive because of trochę.

Because potrzeba already works as the predicate of the sentence. Polish does not need an extra is/are here.

So the structure is simply:

• Na dobry posiłek potrzeba...

A different pattern would be:

• Kilka prostych składników jest potrzebnych.

That is possible, but it is a different way of building the sentence.

Because this construction is impersonal. Potrzeba does not agree with the number of the thing needed.

So even though kilku prostych składników is plural in meaning, potrzeba stays the same.

It helps to think of it as:

• there is a need for several simple ingredients

rather than:

• several simple ingredients are needed

Yes, in many contexts you could.

• Na dobry posiłek trzeba kilku prostych składników.
• Na dobry posiłek potrzeba kilku prostych składników.

Both are understandable and natural. Potrzeba can sound a bit more formal or stylistic, while trzeba is very common in everyday speech.

Yes. Polish word order is flexible.

The sentence begins with Na dobry posiłek to set up the purpose first: for a good meal. That sounds natural and gives the sentence a nice flow.

You could also say:

• Potrzeba kilku prostych składników na dobry posiłek.

That is also understandable, but the emphasis shifts slightly. The original version foregrounds the idea of a good meal first.