После ужина стоит вытереть столешницу, чтобы на кухне был порядок.

Because после requires the genitive case.

The noun ужин changes like this:

• nominative: ужин
• genitive: ужина

So после ужина means after dinner. This is a very common pattern:

• после работы — after work
• после урока — after the lesson
• после фильма — after the film

Стоит + infinitive means something like:

• it’s worth doing
• it’s a good idea to do
• one should do

So стоит вытереть столешницу is softer than нужно or надо. It sounds like practical advice rather than a strict necessity.

Compare:

• Нужно вытереть столешницу — it is necessary to wipe the countertop
• Стоит вытереть столешницу — it would be a good idea to wipe the countertop

Вытереть is perfective, so it focuses on a completed result: wiping the surface clean.

That fits this sentence well, because the idea is to do one complete action after dinner.

• вытереть — to wipe off, to wipe clean, to finish wiping
• вытирать — to wipe, to be wiping, to wipe regularly/habitually

If you said стоит вытирать столешницу после ужина, that would sound more like a general habit or routine: it’s a good idea to wipe the countertop after dinner.
The original sentence emphasizes the completed action a bit more.

Because столешницу is the direct object of вытереть, so it goes in the accusative case.

The noun changes like this:

• nominative: столешница
• accusative: столешницу

This is the normal pattern for many feminine nouns ending in -а:

• книга → книгу
• лампа → лампу
• машина → машину

Столешница means the surface/top of a table or counter. In a kitchen context, it usually means the countertop or worktop, not the whole table.

So the sentence is specifically about wiping the surface, not moving or cleaning an entire piece of furniture.

Чтобы introduces a purpose clause. Here it means:

• so that
• in order that

So:

• После ужина стоит вытереть столешницу, чтобы на кухне был порядок.

means that wiping the countertop is done for the purpose of keeping the kitchen tidy.

This is a very common Russian structure:

• Я открыл окно, чтобы проветрить комнату.
• Мы пришли пораньше, чтобы всё успеть.

Yes, был looks like a past-tense form, but after чтобы this is completely normal.

Russian often uses a past-form verb after чтобы to express:

• purpose
• desire
• intended result
• something wanted rather than something already real

So чтобы ... был порядок means so that there would be order / so that things would be tidy.

It does not mean the action is actually in the past.

Also, был agrees with порядок, which is masculine singular:

• был порядок
• была тишина
• было тепло
• были гости

Because порядок is the grammatical subject of the clause чтобы на кухне был порядок.

Literally, that part is something like:

• so that there was order in the kitchen
• more natural English: so that the kitchen would be tidy

Russian often expresses this idea with a noun like порядок rather than with an adjective alone.

In everyday Russian, на кухне is the normal way to say in the kitchen.

This is partly just idiomatic usage: with some locations, Russian prefers на, even where English uses in.

So:

• на кухне — in the kitchen
• на работе — at work
• на улице — outside / on the street

В кухне is much less natural in ordinary speech and may sound unusual or overly literal in most contexts.

Also, after на in the meaning of location, кухня becomes кухне in the prepositional case.

Because this is an impersonal recommendation.

Russian often leaves out the person when the sentence means something general like:

• one should
• it’s worth
• it’s a good idea

So стоит вытереть столешницу does not say exactly who should do it. It presents the action as sensible in general.

This is very common in Russian instructions, advice, and everyday comments.

Because чтобы на кухне был порядок is a subordinate clause explaining the purpose of the main clause.

Russian normally separates this kind of clause with a comma:

• Я позвонил, чтобы всё объяснить.
• Мы ушли раньше, чтобы не опоздать.
• После ужина стоит вытереть столешницу, чтобы на кухне был порядок.

So the comma here is standard.

Yes. Russian word order is flexible, although some versions sound more natural depending on emphasis.

For example, you could also say:

• Чтобы на кухне был порядок, после ужина стоит вытереть столешницу.

That puts more emphasis on the goal first: so that the kitchen stays tidy...

The original order is very natural because it gives:

1. the advice
2. then the reason or purpose

So it flows well in everyday speech.