Der bliver lagt nye træningsmåtter i rummet i næste uge, fordi de gamle ikke er behagelige længere.

Here Der is a dummy subject. It does not mean there in the literal location sense.

In Danish, der is often used at the beginning of sentences when you introduce that something happens or exists, especially in passive constructions:

• Der bliver lagt nye træningsmåtter ...
• literally something like There are being laid new training mats ...

A more natural English equivalent is just:

• New training mats will be put in the room ...

So der is mainly there because Danish likes to fill the subject position, even when there is no real subject like in English.

Bliver lagt is a passive construction.

• bliver = becomes / is
• lagt = past participle of lægge = lay / put / place

Together, bliver lagt means:

• is being placed
• will be put
• will be laid

In this sentence, the natural translation is will be put/laid, because i næste uge makes it future in meaning.

So although bliver is present tense in form, the whole sentence refers to a future event.

That is very normal in Danish. Danish often uses the present tense when a future time expression makes the time clear.

Here:

• bliver lagt = present passive form
• i næste uge = next week

Because next week is already stated, Danish does not need a separate future tense form the way English often prefers will.

This is very common:

• Jeg rejser i morgen. = I’m leaving tomorrow.
• De kommer på fredag. = They’re coming on Friday.

So the future meaning comes from the time phrase, not from a special future ending.

Because the sentence is passive, not active.

Compare:

• De lægger nye træningsmåtter i rummet.
  = They put new training mats in the room.
  This is active.

• Der bliver lagt nye træningsmåtter i rummet.
  = New training mats are being put / will be put in the room.
  This is passive.

In the passive with blive, Danish uses:

• bliver
  • past participle

So:

• infinitive: lægge
• past participle: lagt

That is why you get bliver lagt, not bliver lægger.

Yes, you could. Danish has two common ways to make the passive:

1. blive-passive

   • Der bliver lagt nye træningsmåtter ...

2. -s passive

   • Der lægges nye træningsmåtter ...

Both are possible here.

Very roughly:

• blive-passive often sounds a bit more like an actual event/process
• -s passive can sound a bit more formal, neutral, or written

In everyday modern Danish, bliver lagt is extremely common and very natural.

Because nye træningsmåtter is indefinite plural.

In English, you can say:

• new training mats

with no article.

Danish works the same way here:

• nye træningsmåtter = new training mats

If it were definite, you would get something like:

• de nye træningsmåtter = the new training mats

So the lack of an article simply means the mats are being mentioned as some new mats, not the specific new mats.

Because they are describing plural nouns.

• nye træningsmåtter
  træningsmåtter is plural, so the adjective is nye

• de gamle
  this refers to the old ones, plural

• behagelige
  this describes something plural as well: the old mats

A very simplified rule is:

• singular common gender indefinite: often basic form
  
  • en ny måtte
• neuter singular indefinite: often -t
  
  • et nyt rum
• plural or definite: often -e
  
  • nye måtter
  • de gamle måtter
  • behagelige måtter

So the -e ending is a normal plural/definite adjective ending.

De gamle means the old ones.

Danish often leaves out a noun when it is already understood from the context. Since the sentence has already mentioned træningsmåtter, Danish can simply say:

• de gamle = the old ones

This is very natural and works like English:

• I like the new mats, but the old ones are uncomfortable.

So de gamle is short for:

• de gamle træningsmåtter

Because fordi introduces a subordinate clause, and in subordinate clauses Danish normally puts ikke before the finite verb.

So:

• main clause: De gamle er ikke behagelige.
• subordinate clause: ... fordi de gamle ikke er behagelige.

This is a very important Danish word-order rule.

Compare:

• Han kommer ikke. = main clause
• ... fordi han ikke kommer. = subordinate clause

So after fordi, ikke usually comes before the verb.

Ikke ... længere means no longer.

So:

• de gamle ikke er behagelige længere = the old ones are no longer comfortable

This is a very common Danish pattern:

• Jeg bor ikke her længere.
  = I don’t live here anymore / no longer live here.

• Han arbejder ikke der længere.
  = He doesn’t work there there anymore.

In this sentence, it suggests that the old mats may once have been comfortable, but that is not true now.

Because they express two different things:

• i rummet = in the room → place
• i næste uge = next week / in the next week → time

So one tells you where something happens, and the other tells you when it happens.

The order here is very natural in Danish:

• place
  • time
• i rummet i næste uge

Danish word order for adverbials can sometimes vary, but this order is common and sounds quite neutral.

Yes. Danish very often forms compound nouns as one word.

So:

• træning = training
• måtte = mat

Together:

• træningsmåtte = training mat
• træningsmåtter = training mats

This is extremely normal in Danish. English often writes similar ideas as two words, but Danish usually prefers one compound word.

Other examples:

• fodboldbane = football field
• soveværelse = bedroom
• arbejdsdag = workday

So træningsmåtter as one word is exactly what you should expect in Danish.

This is a very common problem for learners.

• lægge = to lay / put / place something
  It usually takes an object.
• ligge = to lie / be lying somewhere
  It usually does not take an object.

Examples:

• Jeg lægger bogen på bordet.
  = I put the book on the table.

• Bogen ligger på bordet.
  = The book is lying on the table.

In your sentence, the mats are being put down/placed, so Danish uses lægge, and in the passive that becomes:

• bliver lagt

So if the meaning is to place something, think lægge. If the meaning is to be in a lying position, think ligge.