Bogen står på hylden over bordet, og min hjelm ligger på hylden ved døren.

Those endings mark the definite form in Danish, which usually corresponds to the in English.

• en bog = a book

• bogen = the book

• en hylde = a shelf

• hylden = the shelf

• et bord = a table

• bordet = the table

• en dør = a door
• døren = the door

A very important difference from English is that Danish often puts definiteness at the end of the noun instead of using a separate word like the.

Because the sentence is talking about the book, not just a book.

So:

• en bog = a book
• bogen = the book

In this sentence, the speaker seems to mean a specific book that is already known from context, so Danish uses the definite form bogen.

Because in Danish, a possessive like min usually replaces the definite ending.

So you say:

• min hjelm = my helmet

not

• min hjelmen

This is similar to English: you say my helmet, not my the helmet.

The same pattern works with other possessives:

• min bog = my book
• din dør = your door
• vores bord = our table

Danish very often uses position verbs where English would simply use is.

Here:

• står literally means stands
• ligger literally means lies

Danish chooses these verbs based on how something is positioned or conceived:

• Bogen står suggests the book is standing upright, for example on a shelf.
• min hjelm ligger suggests the helmet is lying/resting horizontally on the shelf.

This is very natural in Danish. English usually just says the book is on the shelf, but Danish often prefers a more specific verb.

Yes, it is grammatically possible, but it is usually less natural in ordinary Danish.

• Bogen er på hylden = The book is on the shelf
• Bogen står på hylden = more idiomatic Danish if the book is upright

Danish often prefers står, ligger, sidder, and similar verbs instead of the more general er. Using er is not necessarily wrong, but it can sound less precise or less native-like.

They describe two different kinds of location:

• over bordet = above the table
• ved døren = by/near the door

So:

• hylden over bordet means the shelf above the table
• hylden ved døren means the shelf by the door

Over tells you something is higher than something else. Ved tells you something is next to or near something else.

På usually means on in this kind of context.

So:

• på hylden = on the shelf

This matches English quite closely here. Danish commonly uses på for things resting on surfaces, including shelves.

In this sentence, over bordet most naturally describes the shelf, not the book.

So the structure is:

• på hylden over bordet
• literally: on the shelf above the table

That means:

1. the book is on the shelf
2. that shelf is above the table

So over bordet attaches to hylden.

Because the sentence joins two full clauses:

1. Bogen står på hylden over bordet
2. min hjelm ligger på hylden ved døren

Each part has its own subject and verb:

• Bogen
  • står
• min hjelm
  • ligger

In Danish, it is normal to put a comma between two main clauses like this before og.

Because hjelm is a common gender noun in Danish.

Danish has two grammatical genders:

• common gender → uses en in the indefinite form, and possessives like min
• neuter → uses et in the indefinite form, and possessives like mit

Since it is:

• en hjelm = a helmet

you get:

• min hjelm = my helmet

Compare with a neuter noun:

• et bord = a table
• mit bord = my table

Not necessarily. The sentence does not strongly suggest they are the same shelf.

The two shelves are identified differently:

• hylden over bordet
• hylden ved døren

That makes them sound like two different shelves in two different places.

If context made it clear there was only one shelf, a listener might interpret it that way, but the most natural reading is that these are separate shelves.

Yes, very possibly.

Danish often changes the verb depending on position:

• Bogen står på hylden = the book is standing upright
• Bogen ligger på hylden = the book is lying flat on the shelf

This is one of the things English speakers often need time to get used to, because English usually uses is in both cases, while Danish prefers a more specific verb.