На стене в ванной есть крючок, на котором висит полотенце.

Both На стене в ванной and В ванной на стене are possible.

Russian word order is flexible, so the speaker can choose what to present first. Here, На стене puts the wall first as the location being described, and в ванной then narrows it down: on the wall in the bathroom.

So the opening works like:

• На стене = on the wall
• в ванной = in the bathroom

Together: On the wall in the bathroom...

The meaning does not change much if you switch them, but the emphasis shifts slightly.

Because after на when it means on in the sense of location, Russian uses the prepositional case.

• стена = wall
• на стене = on the wall

Compare:

• на стене = on the wall, located there
• на стену = onto the wall, movement toward it

So in this sentence, the hook is already located there, so на стене is correct.

Yes. В ванной is short for в ванной комнате.

• ванная комната = bathroom
• ванная by itself often means bathroom in everyday speech

Grammatically, ванной here is the prepositional singular form, because it follows в in a location meaning:

• ванная = bathroom / bath-related room
• в ванной = in the bathroom

So although it originally comes from an adjective, it is very commonly used like a noun.

Here есть means there is / there exists.

So:

• Есть крючок = there is a hook

Russian often uses есть when introducing the existence of something in a place.

The structure is very common:

• У меня есть книга. = I have a book.
• На столе есть чашка. = There is a cup on the table.

In some contexts, Russian can omit есть, but here it sounds natural because the sentence is presenting the existence of the hook.

Because it is the thing being said to exist.

In the pattern [location] + есть + [thing], the thing normally appears in the nominative:

• крючок = hook

So:

• На стене в ванной есть крючок = On the wall in the bathroom there is a hook

The location phrase comes first, but крючок is still grammatically the main noun of that clause.

Literally, it means on which.

It refers back to крючок:

• крючок = hook
• на котором = on which

So the second part says:

• на котором висит полотенце = on which a towel is hanging

In natural English, we usually say a hook with a towel hanging on it or a hook on which a towel is hanging.

Because the relative pronoun has to match the grammar of its role inside the relative clause.

The noun it refers to is крючок, which is:

• masculine
• singular

That is why we get a masculine singular form of который.

But inside the clause, the phrase is на котором because the towel is hanging on the hook. After на with location, Russian uses the prepositional case.

So:

• base form: который
• prepositional masculine/neuter singular: котором

Hence:

• на котором = on which

Because the towel is not the subject hanging by itself in relation to the hook; it is hanging on the hook.

Russian expresses that relationship explicitly with на:

• полотенце висит на крючке = the towel is hanging on the hook

When that becomes a relative clause, на крючке turns into на котором:

• крючок, на котором висит полотенце = the hook on which the towel is hanging

So на must stay there because it is part of the meaning.

Висит is the 3rd person singular form of висеть = to hang.

The subject is полотенце:

• полотенце = towel
• it is grammatically singular
• so the verb is singular: висит

Compare:

• Полотенце висит. = The towel is hanging.
• Полотенца висят. = The towels are hanging.

Because nouns in Russian have grammatical gender, and полотенце is a neuter noun.

A common clue is the ending:

• many neuter nouns end in -о or -е
• полотенце ends in -е, so it is neuter

That affects agreement:

• большое полотенце = a big towel
• чистое полотенце = a clean towel

And with verbs in the present tense, gender does not show, but in the past it would:

• полотенце висело = the towel was hanging

Yes, but the nuance changes a little.

• На стене в ванной есть крючок... clearly introduces the existence of a hook.
• На стене в ванной крючок... sounds less natural in this context unless the sentence continues in a special way or the context strongly supports it.

So есть is the normal, safe choice here.

Russian often omits есть in present-tense identity statements:

• Это мой брат. = This is my brother.

But for there is / there are meanings, есть is very common.

Крючок is a general word for hook.

Depending on context, it can mean:

• a wall hook
• a small metal hook
• a crochet hook
• even a fishhook in some contexts

Here, because it is on the wall in the bathroom and a towel is hanging on it, it clearly means a wall hook or towel hook.

Not naturally in this sentence.

Russian needs the subject here:

• на котором висит полотенце = on which a towel is hanging

If you remove полотенце, you get:

• на котором висит

That sounds incomplete unless the missing subject has just been mentioned and is fully recoverable from context. In a standalone sentence, you would normally keep полотенце.

A very literal breakdown would be:

• На стене = on the wall
• в ванной = in the bathroom
• есть = there is
• крючок = a hook
• на котором = on which
• висит = hangs / is hanging
• полотенце = a towel

So, almost word for word:

On the wall in the bathroom there is a hook, on which hangs a towel.

That is not the most natural English, but it shows how the Russian sentence is built.