Pak så let som muligt, for bagagerummet er allerede fyldt, og reservedækket tager også plads.

Pak is the imperative form of pakke = to pack.

So Pak så let som muligt means Pack as lightly as possible or Pack as light as possible.

In Danish, the imperative usually has no written subject, but du is understood:

• (Du) pak! = (You) pack!

This form can be a command, advice, or a practical instruction.

This is a very common Danish pattern:

så + adjective/adverb + som muligt
= as ... as possible

So:

• så let som muligt = as lightly as possible / as light as possible

Other examples:

• så hurtigt som muligt = as quickly as possible
• så snart som muligt = as soon as possible
• så præcist som muligt = as precisely as possible

It is a fixed and very useful structure.

Because let here means lightly / with little weight, which is the natural idea when talking about packing.

So:

• pak let = pack light
• pak lidt would mean something more like pack a little, which is a different idea

A learner might think of English pack as little as possible, but Danish normally expresses this with let, not lidt, when the point is that the luggage should not weigh much or take much room.

Here let is being used adverbially, after the verb pak.

Danish often uses the -t form of an adjective when it functions like an adverb:

• han taler højt = he speaks loudly
• de kører hurtigt = they drive quickly
• pak let = pack lightly / pack light

So let is the natural form here.
Lette would not fit this structure.

Yes, for often means for, but in Danish it can also mean because / for, introducing an explanation.

In this sentence:

• Pak så let som muligt, for bagagerummet er allerede fyldt
  means
• Pack as lightly as possible, because the trunk is already full

This for is a coordinating conjunction. It links two main clauses and gives a reason.

A close alternative would be fordi, but there is a grammatical difference:

• for bagagerummet er allerede fyldt
• fordi bagagerummet allerede er fyldt

With for, the clause clearly keeps normal main-clause word order.

Bagagerummet means the trunk or the luggage compartment.

It comes from the noun:

• et bagagerum = a trunk / a luggage compartment
• bagagerummet = the trunk / the luggage compartment

It is a compound noun:

• bagage = luggage
• rum = room / compartment

As in many Danish compounds, only the last part changes for definiteness.
So the whole word becomes bagagerummet = the luggage compartment.

Er allerede fyldt is the most neutral and standard word order.

In a Danish main clause, an adverb like allerede usually comes:

• after the finite verb
• before the predicate adjective or participle

So:

• bagagerummet er allerede fyldt

This is the normal pattern.

You can sometimes hear:

• bagagerummet er fyldt allerede

but that sounds more marked or emphatic. The sentence you were given uses the most natural everyday order.

Fyldt is the past participle of fylde = to fill.

In this sentence, it works like an adjective:

• er fyldt = is filled / is full

So bagagerummet er allerede fyldt literally means:

• the trunk is already filled

In natural English, that is often just:

• the trunk is already full

This is a very common Danish pattern:

• Døren er lukket = The door is closed
• Glasset er fyldt = The glass is full / filled

Reservedækket means the spare tire.

The basic noun is:

• et reservedæk = a spare tire
• reservedækket = the spare tire

It is another compound noun:

• reserve- = spare / reserve
• dæk = tire

Yes, it is understandable and correct. In some contexts, Danish speakers may also use other car-related words depending on exactly what they mean, but reservedæk is a normal word for spare tire.

Tager plads literally means takes space, and in natural English that is usually takes up space.

So:

• reservedækket tager også plads = the spare tire also takes up space

The adverb også = also is placed in the normal Danish position for a main clause:

• subject: reservedækket
• finite verb: tager
• adverb: også
• rest: plads

So the word order is completely standard.

Because the sentence contains several full clauses:

• Pak så let som muligt
• for bagagerummet er allerede fyldt
• og reservedækket tager også plads

In Danish, commas are often used to separate coordinated clauses, especially when each part has its own verb.

So the commas help show the structure:

1. instruction
2. reason
3. extra reason

That is why the punctuation looks fuller than it might in some English sentences.