W zlewie jest za dużo naczyń, więc nie mam zamiaru gotować teraz obiadu.

Because w meaning in takes the locative case when it describes location.

• zlew = sink
• w zlewie = in the sink

So this is a normal case change:

• nominative: zlew
• locative: w zlewie

Polish has no articles, so there is no direct equivalent of a / an / the.

Whether something is definite or indefinite is understood from context. So:

• w zlewie can mean in the sink
• naczynia can mean dishes or the dishes

In this sentence, the context makes it clear that we mean the dishes in the sink.

Because the grammatical focus is the quantity expression za dużo naczyń = too many dishes.

In Polish, expressions with words like dużo, mało, sporo, mnóstwo often take a singular neuter verb, even when the noun refers to many things.

So Polish says:

• Jest za dużo naczyń not
• Są za dużo naczynia

Similar patterns:

• Jest dużo ludzi = There are many people
• Było mało czasu = There was little time

After quantity expressions like dużo, mało, za dużo, trochę, the noun usually goes into the genitive.

So:

• naczynia = nominative/accusative plural
• naczyń = genitive plural

That is why:

• dużo naczyń = a lot of dishes
• za dużo naczyń = too many dishes

This is a very common pattern in Polish.

No.

• dużo = a lot / many
• za dużo = too much / too many

So za dużo adds the idea of excess or more than is acceptable.

Compare:

• W zlewie jest dużo naczyń = There are a lot of dishes in the sink
• W zlewie jest za dużo naczyń = There are too many dishes in the sink

A slightly more formal alternative is zbyt dużo.

Here naczynia means dishes, especially dirty dishes in the sink.

It is a broad word and can include things like:

• plates
• bowls
• cups
• glasses
• sometimes other kitchen items

So it is wider than just plates.

Więc means so, therefore, or so then.

It introduces the result of the first clause:

• W zlewie jest za dużo naczyń = There are too many dishes in the sink
• więc nie mam zamiaru... = so I don’t intend...

The comma is standard because two clauses are being linked:

• clause 1: W zlewie jest za dużo naczyń
• clause 2: nie mam zamiaru gotować teraz obiadu

Nie mam zamiaru + infinitive means I do not intend to... or I have no intention of...

So:

• nie mam zamiaru gotować = I do not intend to cook

It is usually a bit stronger and more deliberate than simply I don’t want to. It can sound like:

• a decision
• a refusal
• sometimes mild annoyance

So in this sentence it feels like: There are too many dishes in the sink, so I’m not going to cook dinner now.

Because of negation.

The basic expression is:

• mam zamiar = I intend / I have the intention

But after nie mam, Polish normally uses the genitive:

• nie mam zamiaru = I do not intend / I have no intention

So this is a classic example of genitive after negation.

It can mean both, depending on context.

• gotować wodę = to boil water
• gotować obiad = to cook dinner / make a meal

In this sentence, gotować clearly means to cook / prepare a meal, not just to boil something.

Because after mieć zamiar or nie mieć zamiaru, Polish uses an infinitive for the action intended.

Pattern:

• mam zamiar + infinitive
• nie mam zamiaru + infinitive

Examples:

• Mam zamiar odpocząć = I intend to rest
• Nie mam zamiaru czekać = I do not intend to wait

So:

• nie mam zamiaru gotować = I do not intend to cook

Obiadu is the genitive singular of obiad.

The basic dictionary phrase is usually:

• gotować obiad = to cook dinner / lunch

But in a sentence with a negated higher verb such as nie mam zamiaru gotować..., Polish often uses the genitive for the object of the infinitive as well:

• nie mam zamiaru gotować obiadu

So this is another place where negation influences case choice. For a learner, the safest thing to remember is:

• base phrase: gotować obiad
• in this negated structure, gotować obiadu is very natural

It depends on context and on cultural habits.

In Polish, obiad is usually the main cooked meal of the day, often eaten in the afternoon. Because of that, English translations vary:

• lunch in some contexts
• dinner in others

So when you see obiad, think first of the main meal, not of an exact English meal label.

Yes. Polish word order is more flexible than English.

Here:

• gotować teraz obiadu

puts teraz in a natural position meaning now / at the moment.

Other word orders are also possible, for example:

• nie mam zamiaru teraz gotować obiadu
• teraz nie mam zamiaru gotować obiadu

The meaning stays similar, but the emphasis shifts slightly. In the original sentence, teraz naturally highlights not now.