На подоконнике у меня стоят кактус, фикус и орхидея.

Because на here means on in the sense of location, so it takes the prepositional case.

• Dictionary form: подоконник = windowsill
• Prepositional singular: подоконнике

So:

• на подоконнике = on the windowsill

If you were talking about motion onto the windowsill, you would use the accusative:

• поставить на подоконник = to put onto the windowsill

У меня literally means by me / at my place, and меня is in the genitive case after у.

Russian often uses у + genitive to express possession or something existing at someone's place, instead of using a verb exactly like English have.

So:

• у меня есть книга = I have a book
• у меня на подоконнике стоят... = I have ... on my windowsill / On my windowsill, there are ...

Here у меня helps show that this is my windowsill / at my place, without needing a separate word for my.

Russian often prefers position verbs when describing where things are:

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

Potted plants are thought of as standing upright, so стоят sounds natural.

That is why Russian says:

• На подоконнике стоят кактус, фикус и орхидея.

English usually just says are, but Russian is often more specific about position.

Because the subject is not just кактус. The full subject is the whole list:

• кактус, фикус и орхидея

That means a cactus, a ficus, and an orchid — three separate things together — so the verb must be plural:

• стоят = stand / are standing

If there were only one plant, you would use singular:

• На подоконнике стоит кактус.

Because the sentence names one of each plant:

• кактус = a cactus
• фикус = a ficus
• орхидея = an orchid

Russian often lists items this way in the singular when it means one X, one Y, and one Z.

If you used plurals, it would suggest multiple cacti, multiple ficuses, and multiple orchids, or speak about those kinds of plants more generally.

This can feel strange to English speakers because Russian has no articles. Even though there is no word for a, the singular noun often carries that idea from context.

They are in the nominative case, because they are the things doing the action of standing in the sentence.

Even though they come after the verb, they are still the grammatical subject.

So the structure is basically:

• На подоконнике = location
• у меня = at my place / I have
• стоят = stand
• кактус, фикус и орхидея = the subjects

Russian word order is flexible, so the subject does not always have to come first.

Because Russian usually does not use есть in ordinary present-tense location sentences when another verb is already doing the job.

Here, стоят already tells you that the plants are there and describes their position.

So Russian says:

• На подоконнике у меня стоят кактус, фикус и орхидея.

not:

• На подоконнике у меня есть стоят... ❌

You do use есть in sentences like:

• У меня есть кактус. = I have a cactus.

But once you say where it is and use a location verb like стоит, есть is not needed.

Yes. Russian word order is fairly flexible, and changing it usually changes emphasis, not the core meaning.

For example:

• На подоконнике у меня стоят кактус, фикус и орхидея.

  • neutral; starts with the location

• У меня на подоконнике стоят кактус, фикус и орхидея.

  • slightly emphasizes at my place / on my windowsill

• Кактус, фикус и орхидея стоят у меня на подоконнике.

  • emphasizes the plants themselves first

The version in your sentence is very natural because it sets the scene first: On the windowsill...

Usually, not in this sentence.

• стоят describes where the plants are and how they are positioned
• растут means grow and focuses on the process of growing

So:

• На подоконнике стоят кактус, фикус и орхидея. = They are standing/sitting there on the windowsill.

• На подоконнике растут кактус, фикус и орхидея. = The plants are growing there.

The second sentence is not impossible, but it has a different focus. If you simply want to say what is on the windowsill, стоят is more natural.

Not exactly.

• подоконник = windowsill
• окно = window

So на подоконнике is the precise phrase for plants physically standing on the sill.

Sometimes Russians do say цветы на окне, and in everyday speech that can mean flowers in the window / on the windowsill. But literally, на окне means on the window, which is less exact.

So for a learner, на подоконнике is the safest and most precise choice here.

Then the sentence just becomes a statement about what is on the windowsill, without clearly saying it is my place.

Compare:

• На подоконнике стоят кактус, фикус и орхидея. = There is a cactus, a ficus, and an orchid on the windowsill.

• На подоконнике у меня стоят кактус, фикус и орхидея. = On my windowsill / at my place, there is a cactus, a ficus, and an orchid.

So у меня adds the idea of mine / at my home / in my space.

With stress marks, it is:

На подоко́ннике у меня́ стоя́т ка́ктус, фи́кус и орхиде́я.

A rough pronunciation guide:

• На подокОннике = na pa-da-KON-ni-kye
• у меня = oo myi-NYA
• стоят = sta-YAT
• кактус = KAK-toos
• фикус = FEE-koos
• орхидея = ar-khee-DYE-ya

The most important thing to remember is the stress, especially in:

• подокОннике
• стоят
• орхидЕя