Min bagage står ved siden af min plads, men hendes håndbagage ligger på hylden over os.

Danish often uses more specific position verbs where English just uses is.

• står = stands / is standing
• ligger = lies / is lying

So:

• Min bagage står ... suggests the luggage is in an upright position.
• hendes håndbagage ligger ... suggests the hand luggage is lying flat on the shelf.

This is very natural in Danish. English usually does not bother to specify position unless it matters.

Sometimes, yes, but it often sounds less natural.

• Min bagage er ved siden af min plads is understandable.
• Hendes håndbagage er på hylden over os is also understandable.

But Danish prefers position verbs like står, ligger, and sometimes sidder when talking about where things are. Using them makes your Danish sound more native-like.

Because bagage and plads are common gender nouns in Danish, so they take min.

Danish singular possessives agree with the gender of the noun:

• min for common gender nouns
• mit for neuter nouns
• mine for plural nouns

So:

• min bagage
• min plads

If the noun were neuter, you would use mit.

In Danish, a possessive usually replaces the article.

So English my luggage and her hand luggage become:

• min bagage
• hendes håndbagage

You normally do not say den min bagage or anything similar here.

Compare:

• bagagen = the luggage
• min bagage = my luggage

You use one or the other, not both in this kind of phrase.

Ved siden af means beside or next to.

It is a fixed Danish expression:

• ved = by / at
• siden = the side
• af = of

But as a learner, it is best to memorize ved siden af as one unit meaning next to.

Examples:

• ved siden af døren = next to the door
• ved siden af mig = next to me

Yes, in this sentence plads means seat, but the word is broader than that.

Plads can mean:

• seat
• place
• space
• room

So min plads could mean my seat here, especially in a plane, train, or bus context.

A related word is sæde, which more literally means seat, but plads is very common when talking about your assigned place.

This is a very common learner question.

Danish uses:

• sin/sit/sine for a possessive that refers back to the subject of the same clause
• hans/hendes/deres when it refers to someone else

In the second clause, the subject is håndbagage? Actually, grammatically the subject is hendes håndbagage as a whole, but the owner is she, not the subject of a separate earlier clause. Since the owner is explicitly her, Danish uses hendes.

Compare:

• Hun tager sin håndbagage. = She takes her own hand luggage.
• Hun tager hendes håndbagage. = She takes another woman’s hand luggage.

In your sentence, hendes håndbagage simply means her hand luggage.

Yes, it is one compound word: håndbagage.

Danish makes compounds very freely, much like German.

• hånd = hand
• bagage = luggage

So håndbagage means hand luggage or carry-on luggage.

English often writes this as two words, but Danish normally writes it as one.

Because hylden is the definite form: the shelf.

• en hylde = a shelf
• hylden = the shelf

So:

• på hylden = on the shelf

Danish often puts the definite article at the end of the noun:

• bil → bilen
• stol → stolen
• hylde → hylden

Over os means above us or over us.

• over = over / above
• os = us

So på hylden over os means on the shelf above us.

This is very natural in a travel context, such as a train or airplane.

Because Danish, like English, uses different pronoun forms for subject and object.

• vi = we
• os = us

After a preposition like over, Danish uses the object form:

• over os
• ved siden af os
• bag os

Just like English says above us, not above we.

Yes. This is normal Danish main-clause word order:

subject + verb + rest

• Min bagage = subject
• står = verb
• ved siden af min plads = rest

Then after men (but), the next clause also has normal main-clause order:

• hendes håndbagage = subject
• ligger = verb
• på hylden over os = rest

So the sentence structure is very straightforward.

Usually bagage works like luggage in English: it is generally an uncountable mass noun.

So:

• min bagage = my luggage
• meget bagage = a lot of luggage

If you want to talk about individual pieces, Danish often uses expressions like:

• en taske = a bag
• en kuffert = a suitcase
• et stykke bagage = a piece of luggage

In context, min bagage might refer to one item or several items, depending on the situation.

A rough guide for an English speaker:

• bagage sounds approximately like ba-GA-she, with the stress on the second syllable.
• håndbagage keeps that same main stress in the -gage part, though pronunciation varies a bit by speaker and region.

A few useful points:

• å in hånd is like a broad aw/o sound.
• The final -ge in many Danish words is often softened, not pronounced like hard English g.

If you are learning pronunciation, it is best to listen to native audio, because Danish spelling and pronunciation do not always match in an obvious way.

Not naturally here.

• over os is the normal choice for above us / over us
• oven over os can exist, but it is more emphatic and often feels heavier, like up above us

In this sentence, på hylden over os is the most natural phrasing.