I omklædningsrummet lægger jeg min taske i skabet og låser det med en hængelås.

No. It is the preposition i, meaning in, but it is capitalized because it starts the sentence.

So:

• i = in
• I omklædningsrummet = In the changing room / locker room

In normal mid-sentence position, it would be written i, not I.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

Here, the sentence starts with I omklædningsrummet, so that first element takes position 1. The verb lægger must then come next, and the subject jeg comes after it:

• I omklædningsrummet = position 1
• lægger = position 2
• jeg = subject after the verb

If you started with the subject instead, you would say:

• Jeg lægger min taske i skabet ...

Because Danish very often forms compound nouns by writing them as one word.

omklædningsrummet is built from:

• omklædning = changing
• rum = room
• plus the definite ending

So the basic noun is:

• et omklædningsrum = a changing room / locker room

And the definite form is:

• omklædningsrummet = the changing room / locker room

This is very normal in Danish. English often writes similar ideas as two words, but Danish usually joins them.

Because Danish usually adds the definite article to the end of the noun.

These are et-words:

• et omklædningsrum = a changing room

• omklædningsrummet = the changing room

• et skab = a cabinet / locker
• skabet = the cabinet / locker

So instead of putting the in front, Danish often adds a suffix:

• en-word definite: -en
• et-word definite: -et

That is why you see -et here.

Because taske is an en-word:

• en taske = a bag

For singular possessives, Danish uses:

• min with en-words
• mit with et-words
• mine with plurals

So:

• min taske = my bag
• mit skab = my locker / my cabinet
• mine tasker = my bags

det refers to skabet, not min taske.

That makes sense both logically and grammatically:

• logically, you lock the locker, not the bag
• grammatically, skab is an et-word, so the pronoun is det

Compare:

• et skab → det
• en taske → den

So if you were referring to tasken, you would expect den, not det.

Because Danish can leave out the repeated subject when two verbs share the same subject and are linked by og.

So:

• I omklædningsrummet lægger jeg min taske i skabet og låser det ...

means that jeg is understood for both lægger and låser.

You could also say:

• I omklædningsrummet lægger jeg min taske i skabet, og jeg låser det med en hængelås.

That is also correct, but it sounds a little more explicit or slightly heavier. The version without the second jeg is very natural.

Because lægge is the normal verb for laying/putting something down.

Danish often distinguishes between different kinds of put verbs:

• lægge = lay/put down, often for something lying flat
• stille = put/stand something upright
• sætte = set/place, often something in a sitting position or more generally in many contexts
• putte = put/stick something into something, often more casually

With a bag, lægge is very natural here:

• lægger jeg min taske i skabet

A Danish speaker might also say putter min taske i skabet in some situations, but lægger is completely normal.

In Danish, i can often cover both in and into, depending on the verb and context.

Here:

• I omklædningsrummet = location, in the changing room
• lægger ... i skabet = movement into the locker, so in English you might think into the locker

Danish does not always need a separate word for into. The verb lægger already shows movement, so i skabet is enough.

If you want to emphasize movement inward, Danish can also use ind i, but it is not necessary here.

med means with, and here it shows the means or tool used:

• låser det med en hængelås = lock it with a padlock

en hængelås is indefinite because it means a padlock, not the padlock.

Also, hængelås is another compound noun:

• hænge = hang
• lås = lock

So en hængelås is literally a kind of hanging lock, which is why it means a padlock.

Because Danish, like English, can use the definite form when the thing is understood from the situation.

In a changing room or locker room, skabet naturally means something like:

• the locker
• the relevant locker
• the locker I am using

So it does not have to mean that the locker was already mentioned earlier in the conversation. It can simply be definite because the context makes it identifiable.

It is in the present tense:

• lægger
• låser

In Danish, the present tense can describe:

• something happening now
• a habitual action
• a general routine
• a vivid narration

So this sentence could mean something like a routine action: this is what I do in the changing room.

Yes. skab has a broad meaning: it can be a cabinet, cupboard, or locker depending on context.

So:

• et skab can mean different kinds of enclosed storage furniture
• in omklædningsrummet, the most natural meaning is locker

That is very common in Danish: the surrounding context tells you which English word fits best.