На подоконнике стоят кактус, фикус и орхидея.

Because after на meaning on in a location sense, Russian uses the prepositional case.

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

So:

• на подоконнике = on the windowsill / at the windowsill

If there were motion onto the windowsill, Russian would use a different case:

• поставить на подоконник = to put onto the windowsill

So the sentence uses подоконнике because it describes where the plants are, not movement.

Russian uses на because a windowsill is treated as a surface, and things stand on a surface.

• на столе = on the table
• на полке = on the shelf
• на подоконнике = on the windowsill

By contrast, в usually means in / inside something:

• в комнате = in the room
• в коробке = in the box

So на подоконнике is the natural choice because the plants are sitting on top of the windowsill.

Because the subject is plural overall: there are three things named:

• кактус
• фикус
• орхидея

Together they form a plural subject, so the verb must be plural:

• стоят = are standing

Compare:

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

Even though each noun is singular individually, the whole list is plural.

Because they are the subject of the sentence, so they are in the nominative case.

Russian marks grammatical roles by case. Here:

• На подоконнике = location phrase
• стоят = verb
• кактус, фикус и орхидея = the things doing the “standing,” so they are the subject

That is why they appear in their dictionary-like forms:

• кактус
• фикус
• орхидея

Russian often uses position verbs where English would simply say is/are.

For objects in an upright position, Russian commonly uses:

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

Plants in pots are normally thought of as standing, so:

• На подоконнике стоят цветы. = There are flowers on the windowsill.

In English, stand may sound too literal here, but in Russian it is very natural.

Yes, in some contexts Russian can omit a verb in present-tense descriptions, especially in informal or compressed speech. But стоят sounds more natural and complete here because it expresses the normal position of the objects.

Compare:

• На подоконнике кактус, фикус и орхидея.
  More like a simple listing or noting what is there.

• На подоконнике стоят кактус, фикус и орхидея.
  A fuller, more natural sentence describing the scene.

So the version with стоят is a very standard way to say it.

Yes. Russian word order is more flexible than English because case endings show grammatical roles.

Both are correct:

• На подоконнике стоят кактус, фикус и орхидея.
• Кактус, фикус и орхидея стоят на подоконнике.

The difference is mostly in emphasis:

• На подоконнике стоят... emphasizes the location first.
• Кактус, фикус и орхидея стоят... emphasizes what things are being talked about.

The original sentence sounds very natural if the speaker is describing what is on the windowsill.

This is the normal punctuation for a simple list in Russian, just like in English:

• кактус, фикус и орхидея

Russian normally puts commas between earlier items in a list, but not before the final и when it simply means and.

So this works exactly as you would expect from standard list punctuation.

Орхидея is in the nominative singular, and -я is simply part of its normal dictionary form.

It is a feminine noun, and many feminine nouns end in:

• -а
• -я

So:

• орхидея = orchid

The ending here is not caused by some special rule in this sentence; it is just the noun’s normal nominative singular form.

The standard stresses are:

• на подоко́ннике
• стоя́т
• ка́ктус
• фи́кус
• орхиде́я

So the whole sentence is pronounced roughly like:

На подоко́ннике стоя́т ка́ктус, фи́кус и орхиде́я.

Stress is important in Russian, so it is worth learning words with their stress whenever possible.

It is used for both.

In Russian, стоять can describe:

• people standing upright
• objects that are upright or placed vertically
• many things that English would simply describe with is/are

Examples:

• Человек стоит у окна. = The person is standing by the window.
• Ваза стоит на столе. = The vase is on the table.
• Цветы стоят на подоконнике. = The flowers are on the windowsill.

So using стоят for potted plants is completely normal.

In Russian, есть is not used the same way English uses there is / there are in ordinary location sentences.

Russian usually just says the location plus the noun, often with a suitable verb like стоять, лежать, or висеть.

So instead of literally saying There are a cactus, a ficus, and an orchid on the windowsill, Russian naturally says:

• На подоконнике стоят кактус, фикус и орхидея.

That is one of the standard ways Russian expresses existence/location.