Капсула для стирки лежит рядом с корзиной для белья.

Because the preposition для normally takes the genitive case in Russian.

So:

• стирка → стирки
• бельё → белья

This is a very common pattern: для + genitive = for + noun. In this sentence, both phrases show purpose: для стирки and для белья.

Because рядом с requires the instrumental case.

The base form is корзина, but after рядом с it becomes корзиной. So the pattern is:

рядом с + instrumental = next to / beside

This is something you just have to learn as a set expression: рядом с кем? чем?

Not really on its own. In this sentence, с is part of the fixed expression рядом с, which means next to or beside.

So you should learn рядом с as one unit. Even though с often means with, here the whole phrase has a different meaning.

Капсула is in the nominative case because it is the subject of the sentence.

It is the thing that is doing the action of лежит. In Russian, the subject is usually in the nominative, just as in many basic sentences:

• Книга лежит...
• Капсула лежит...

Лежит is the 3rd person singular present tense form of the verb лежать.

So:

• infinitive: лежать
• present: лежит = lies / is lying

It matches the singular subject капсула. Russian present tense does not use a separate word for is in sentences like this.

In Russian, the present-tense verb to be is usually omitted. So instead of saying something like the capsule is next to..., Russian often uses a position verb such as:

• лежать = to lie
• стоять = to stand
• висеть = to hang

So лежит does double work here: it shows both location and physical position. For a small object like a laundry pod, лежит sounds natural if it is resting on a surface.

Sometimes, yes, but the meaning or style changes.

• стоит suggests something is standing upright
• лежит suggests something is lying/resting
• находится is more neutral and often more formal, like is located

For a laundry pod, лежит is the most natural choice in everyday speech. Находится рядом с корзиной is grammatically fine, but less conversational.

They are related, but they do not mean the same thing.

• стирка is the washing process or doing laundry
• бельё is the laundry/clothes/linen themselves

So:

• капсула для стирки = a capsule for washing
• корзина для белья = a basket for laundry/clothes

That is why both nouns are needed: one refers to the activity, the other to the items.

Yes. Russian word order is fairly flexible because the case endings show the grammatical roles.

For example, you could also say:

Рядом с корзиной для белья лежит капсула для стирки.

That version puts more focus on the location first. The original sentence is a neutral, natural order, but Russian often changes word order for emphasis or information flow.

Russian has no articles.

So капсула can mean a capsule or the capsule, depending on context. The same is true for корзина and many other nouns.

English speakers often want to know which one it is, but in Russian the context usually makes it clear.

A stress-marked version is:

Капсу́ла для сти́рки лежи́т ря́дом с корзи́ной для белья́.

The main stressed syllables are:

• капсу́ла
• сти́рки
• лежи́т
• ря́дом
• корзи́ной
• белья́

Stress is very important in Russian, and it is not always predictable, so it is worth learning words together with their stress.

Yes. Возле корзины для белья is also natural and means roughly the same thing.

But notice the grammar changes:

• рядом с
  • instrumental → рядом с корзиной
• возле
  • genitive → возле корзины

So both are correct, but they govern different cases. This is a very common thing in Russian prepositions.