У бабушки в ванной стоит старый таз, в котором она стирает мелкие вещи вручную.

Here у + genitive means something like at Grandma’s place or in Grandma’s home. So у бабушки is not literally by the grandmother in a physical sense. It sets the scene: this basin is in the bathroom at Grandma’s.

This pattern is very common in Russian:

• У бабушки есть сад = Grandma has a garden
• Я был у бабушки = I was at Grandma’s place

So in this sentence, у бабушки в ванной means in Grandma’s bathroom.

Because this sentence describes location, not movement.

• в ванной = in the bathroom where something is
• в ванную = into the bathroom, showing motion toward it

Compare:

• Таз стоит в ванной = The basin is standing in the bathroom
• Я несу таз в ванную = I’m carrying the basin into the bathroom

Also, ванная here is a common short form of ванная комната.

Russian often prefers a positional verb like стоит, лежит, or висит when describing where an object is.

• стоит = stands
• лежит = lies
• висит = hangs

A таз is thought of as something standing upright on its base, so стоит sounds natural.

Using есть here would not be the normal choice. In present-tense Russian, есть is often omitted anyway, and Russian usually sounds more natural with a specific location verb:

• В ванной стоит старый таз = In the bathroom there is an old basin / an old basin stands in the bathroom

You could also say находится, but that sounds more formal or neutral.

Старый таз is in the nominative singular because it is the subject of the verb стоит.

• таз = masculine singular nominative
• старый agrees with таз in gender, number, and case

So the basic structure is:

• старый таз стоит = an old basin stands

Because который agrees with the noun it refers to, and here it refers to таз, not ванной.

• таз is masculine singular
• after в, the relative pronoun must be in the prepositional case
• masculine singular prepositional of который is котором

So:

• таз, в котором... = basin, in which...

If it referred to ванная, then it would be в которой, because ванная is feminine.

It refers to таз.

The phrase means the old basin, in which she washes small items by hand.

That is why the form is masculine: котором matches таз. If the sentence meant the bathroom, in which..., then the form would be feminine: в которой.

Because в котором она стирает мелкие вещи вручную is a relative clause, and Russian separates relative clauses with commas.

So the sentence is divided like this:

• У бабушки в ванной стоит старый таз,
• в котором она стирает мелкие вещи вручную.

This is standard Russian punctuation.

It is included to make the subject of the relative clause clear: she = Grandma.

Russian often can omit subject pronouns when the subject is obvious, but here она helps avoid any ambiguity and makes the sentence smoother.

Without она, you would get:

• ...в котором стирает мелкие вещи вручную

That is possible in some contexts, but it sounds less explicit. With она, it is immediately clear that Grandma is the one doing the washing.

Here the present tense describes a habitual or regular action, not something happening right this second.

So она стирает means something like:

• she washes
• she usually washes
• she does her washing there

Russian present tense often works this way for general habits.

Also, стирать is imperfective, which is the normal aspect for repeated, ongoing, or habitual actions.

Because стирает is the imperfective verb, and imperfective is used for repeated or habitual actions.

• стирает = she washes / she does washing
• постирает = she will wash / she’ll wash it once

This sentence is not about one completed washing event. It describes what she uses the basin for in general, so стирает is the right choice.

In this context, мелкие вещи means small items, especially small pieces of clothing or laundry such as socks, underwear, handkerchiefs, and similar things.

It does not have to mean just random things. In a laundry context, it naturally means small washable items.

Grammatically, мелкие вещи is accusative plural, the direct object of стирает. Because вещи is inanimate, the accusative plural looks the same as the nominative plural here.

Вручную means by hand or manually. It is the normal adverb for saying that something is done without a machine.

So:

• стирает вручную = washes by hand

You could say руками, but that literally means with her hands, and it is less idiomatic in this kind of sentence. For laundry, вручную is the natural choice.

Compare:

• стирать вручную = to hand-wash
• делать что-то руками = to do something with one’s hands

Yes. Russian word order is flexible, and changing it changes emphasis more than basic meaning.

The original sentence starts with location:

• У бабушки в ванной стоит старый таз...

This feels natural because it sets the scene first.

Other possible orders include:

• В ванной у бабушки стоит старый таз...
• Старый таз стоит у бабушки в ванной...

These are all understandable, but they emphasize different parts of the sentence. The original version sounds smooth and natural because it moves from place to object to extra description.