Перед ужином я нарезал огурцы и помидоры для салата.

Because перед in the meaning before requires the instrumental case.

So:

• ужин = dinner
• перед ужином = before dinner

This is a fixed grammar pattern:

• перед уроком = before class
• перед сном = before sleep / before going to bed
• перед поездкой = before the trip

So ужином is the instrumental singular form of ужин.

No. Перед can mean two different things depending on context:

1. before (in time)

   • перед ужином = before dinner

2. in front of (in space)

   • перед домом = in front of the house

In both meanings, it usually takes the instrumental case.
In this sentence, because ужин is an event/time, the meaning is clearly before dinner.

Нарезал is the past tense masculine singular form of нарезать.

Here it means something like:

• cut up
• slice
• chop into pieces

So я нарезал огурцы и помидоры means I sliced/cut up cucumbers and tomatoes.

The form нарезал tells you:

• past tense
• masculine speaker (or masculine subject)

Compare:

• я нарезал = I cut up (said by a man)
• я нарезала = I cut up (said by a woman)
• мы нарезали = we cut up

This is mainly about aspect and meaning nuance.

• резать = to cut, to be cutting
• нарезать = to slice up / cut up into pieces

In a sentence like this, Russian often prefers нарезать because the result matters: the cucumbers and tomatoes got cut up for the salad.

So:

• я резал огурцы can sound like I was cutting cucumbers
• я нарезал огурцы sounds more like I cut up/sliced the cucumbers

In other words, нарезал fits well when you mean a completed preparation step.

They are in the accusative plural because they are the direct objects of нарезал.

However, for inanimate plural nouns in Russian, the accusative plural is usually the same as the nominative plural.

So:

• огурцы = cucumbers
• помидоры = tomatoes

These are both:

• nominative plural
• accusative plural

That is why the forms look unchanged.

Because для always requires the genitive case.

So:

• салат = salad
• для салата = for the salad

Other examples:

• для друга = for a friend
• для работы = for work
• для детей = for children

So салата is the genitive singular form of салат.

It most naturally explains the purpose of cutting the vegetables:

• I cut cucumbers and tomatoes for a salad

So it tells you why the speaker cut them.

In practice, it is understood as:

• the cucumbers and tomatoes were being prepared for salad

Not:

• dinner was for the salad
• the speaker was for the salad

Russian often leaves this kind of relationship to context, and here the meaning is very natural and clear.

Yes, very often.

Russian often drops subject pronouns when the meaning is already clear from context.

So both are possible:

• Перед ужином я нарезал огурцы и помидоры для салата.
• Перед ужином нарезал огурцы и помидоры для салата.

The version with я is still perfectly normal. It may sound a bit more explicit, especially if:

• you are introducing yourself as the doer
• you want slight emphasis on I
• the context benefits from clarity

No, Russian word order is fairly flexible.

The given sentence is neutral and natural:

• Перед ужином я нарезал огурцы и помидоры для салата.

But other orders are possible:

• Я перед ужином нарезал огурцы и помидоры для салата.
• Огурцы и помидоры для салата я нарезал перед ужином.

The meaning stays basically the same, but the emphasis changes.

For example:

• starting with Перед ужином highlights the time frame
• starting with Я highlights the subject
• starting with Огурцы и помидоры highlights what was cut

Yes, but there is a nuance.

• перед ужином = before dinner, often fairly close to dinnertime
• до ужина = before dinner, but more broadly by the time dinner happens or prior to dinner

So both can work, but перед ужином often feels more like:

• right before dinner
• in the time leading up to dinner

While до ужина can sound a bit more like a deadline or boundary:

• sometime before dinner

Because Russian has no articles.

So:

• огурцы can mean cucumbers, the cucumbers, or sometimes even some cucumbers
• для салата can mean for the salad or for a salad

The exact meaning comes from context, not from articles.

In this sentence, English might translate it as either:

• Before dinner, I sliced cucumbers and tomatoes for the salad.
• Before dinner, I sliced cucumbers and tomatoes for a salad.

Which one is best depends on the situation.

By itself, помидоры just means tomatoes in the plural. Russian does not mark the difference between:

• tomatoes
• the tomatoes
• some tomatoes

So the sentence does not tell you exactly how definite they are. Context would decide that.

For example, if everyone already knows which vegetables are being prepared, English might use the:

• I sliced the cucumbers and tomatoes...

If they are just ingredients being introduced, English might use no article or some:

• I sliced cucumbers and tomatoes...
• I sliced some cucumbers and tomatoes...

Only the past-tense verb would change:

• Перед ужином я нарезала огурцы и помидоры для салата.

That is because Russian past tense agrees with gender in the singular:

• нарезал = masculine
• нарезала = feminine
• нарезало = neuter
• нарезали = plural

Everything else in the sentence stays the same.

Here нарезал is used as a perfective-style completed action: the vegetables were cut up as a finished step in preparing the salad.

That matters because Russian aspect often tells you whether you are focusing on:

• the process of doing something, or
• the completed result

In this sentence, the completed result is important:

• the cucumbers and tomatoes ended up sliced

That is why нарезал works so naturally here. It presents the cutting as a completed event before dinner.