Planten står ved vinduet i stuen.

Because planten is the definite form: the plant.

In Danish, the definite article is usually attached to the end of the noun instead of being a separate word before it.

• en plante = a plant
• planten = the plant

So the sentence is talking about a specific plant, not just any plant.

Yes, and this is very natural in Danish.

Danish often uses position verbs for where things are:

• stå = stand
• ligge = lie
• sidde = sit
• hænge = hang

A plant in a pot is usually thought of as being upright, so it står. English normally just says is, but Danish is more specific.

So:

• Planten står ved vinduet sounds natural.
• Planten er ved vinduet is understandable, but less idiomatic if you are simply describing where it is.

Ved here means by, near, or next to.

So ved vinduet means the plant is located near the window, not necessarily touching it and not necessarily in it.

Compare:

• ved vinduet = by the window / near the window
• i vinduet = in the window
• på vinduet would usually not be correct for this meaning

For a plant on a windowsill, Danish may still often say ved vinduet, depending on what you want to emphasize.

Because the nouns have different grammatical genders.

Danish has two main genders:

• common gender: takes en
• neuter: takes et

These two nouns are:

• et vindue = a window
• en stue = a living room

When they become definite, the endings change according to gender:

• vindue → vinduet = the window
• stue → stuen = the living room

So the difference is not random; it follows the gender of each noun.

Because Danish usually puts the at the end of the noun as a suffix.

So instead of saying something like the window, Danish says:

• vinduet

And instead of the living room, Danish says:

• stuen

A separate definite word is used mainly in certain cases, especially when there is an adjective:

• vinduet = the window
• det store vindue = the big window

So in your sentence, no separate the is needed.

The basic order is:

subject + verb + place phrases

So:

• Planten = subject
• står = verb
• ved vinduet i stuen = location

This is a normal Danish main-clause pattern.

Danish is a V2 language, which means the finite verb is normally in the second position in main clauses. In this sentence, the subject comes first, so the verb naturally comes second.

You could also move a location phrase to the front, but then the verb still stays second:

• I stuen står planten ved vinduet.

That is also grammatical.

Most naturally, it describes the whole location, especially the window in the living room.

So ved vinduet i stuen is most naturally understood as:

• by the window
• in the living room

In practice, that also tells you where the plant is, of course. Danish often stacks location phrases from more specific to more general:

• ved vinduet = by the window
• i stuen = in the living room

So the full phrase narrows the location step by step.

Yes, you could, and people would understand you. But står is more natural.

Using er is more neutral and less specific. Using står sounds more like native Danish because it reflects the physical position of the plant.

So:

• Planten står ved vinduet i stuen = more idiomatic
• Planten er ved vinduet i stuen = understandable, but less natural in this context

In modern everyday Danish, stue usually means living room.

Depending on context, it can sometimes feel a bit like sitting room, lounge, or main room, but living room is the usual translation.

You may also see it in compounds, for example:

• dagligstue = living room
• spisestue = dining room

So in this sentence, stuen is best understood as the living room.

Yes, but it changes the meaning.

• ved vinduet = by the window / near the window
• i vinduet = in the window

I vinduet can suggest that the plant is placed in the window area, often on the windowsill or visibly in the window. Ved vinduet is broader and simply means it is by or near the window.

So both are possible, but they are not exactly the same.

You would use the indefinite forms:

• en plante
• et vindue
• en stue

So an indefinite version could be:

En plante står ved et vindue i en stue.

That means a plant is standing by a window in a living room.

In real use, that sentence is a bit more abstract or descriptive, while the original sentence sounds like it refers to a specific, known plant, window, and room.