Hun kigger ned på dammen fra broen.

Kigger means looks in the sense of actively directing your eyes at something. Ser is broader and can mean see or look at, depending on context.

In this sentence, kigger fits well because the person is intentionally looking downward at the pond.

• hun kigger = she is looking
• hun ser = she sees / she looks

So kigger feels a bit more deliberate.

They do different jobs:

• ned adds the direction down
• på introduces what she is looking at: dammen

So kigger ned på dammen means she is looking down at the pond.

If you said just Hun kigger på dammen, that would mean She is looking at the pond, but it would not show that she is above it and looking downward.

Sometimes English speakers worry about that, but here it is clearly physical, not emotional.

In this sentence, kigger ned på means looks down at because of the location phrase fra broen.

For the figurative idea to look down on someone in the sense of thinking you are better than them, Danish more often uses se ned på:

• Hun ser ned på ham = She looks down on him

So here, with kigger and the bridge/pond context, it is just literal.

In Danish, the definite article is often added to the end of the noun.

• dam = pond

• dammen = the pond

• bro = bridge
• broen = the bridge

Both dam and bro are common-gender nouns, so the definite singular ending is -en.

This is one of the big differences from English.

The main dictionary forms are:

• hun = she
• at kigge = to look
• ned = down
• på = on / at
• dam = pond
• fra = from
• bro = bridge

In the sentence:

• kigger is the present tense of at kigge
• dammen is the definite singular of dam
• broen is the definite singular of bro

Because she is looking at the pond as an object or surface, not in it.

• på dammen = at the pond / at the pond’s surface
• i dammen = in the pond

If you said ned i dammen, that would suggest looking down into the pond, focusing more on what is inside the water.
But ned på dammen is the natural choice for simply looking down at the pond from above.

Fra broen means from the bridge and gives the viewpoint or starting point of the looking.

It tells you where she is when she looks down at the pond.

So the structure is roughly:

• Hun kigger = She is looking
• ned på dammen = down at the pond
• fra broen = from the bridge

Because fra broen focuses on the viewpoint: she is looking from the bridge.

• fra broen = from the bridge
• på broen = on the bridge

If you want to stress her physical location, you might say:

• Hun står på broen og kigger ned på dammen.
  = She is standing on the bridge and looking down at the pond.

But in your sentence, fra broen works well because it describes where the looking happens from.

Yes. Kigger is the present tense of at kigge.

A few forms are:

• at kigge = to look
• kigger = looks / is looking
• kiggede = looked / was looking
• har kigget = has looked

Danish verbs do not change for person:

• jeg kigger
• du kigger
• hun kigger

The verb form stays the same.

Because Danish often uses the simple present where English uses the present progressive.

So:

• Hun kigger can mean She looks or She is looking

The context tells you which meaning is intended. In this sentence, the natural English translation is usually She is looking down at the pond from the bridge, even though Danish just uses the simple present form kigger.

Because at is only used with the infinitive, like English to.

• at kigge = to look
• hun kigger = she looks / she is looking

So in a normal finite sentence, you use kigger, not at kigge.

Yes, but the verb still has to stay in second position in a main clause.

The neutral order is:

• Hun kigger ned på dammen fra broen.

You can front another element for emphasis:

• Fra broen kigger hun ned på dammen.

Notice what happens:

• the first element is now Fra broen
• the verb kigger stays second
• the subject hun moves after the verb

That is a very common Danish pattern.

You would put the verb before the subject:

• Kigger hun ned på dammen fra broen?

That means:

• Is she looking down at the pond from the bridge?

This verb-subject order is the normal way to form yes/no questions in Danish.