Jeg anvender min nye færdighed, når jeg oversætter den danske tekst.

Yes, you could also say bruger.

The difference is mainly style:

• anvender = use / apply, and sounds a bit more formal or deliberate
• bruger = use, and is more common in everyday speech

So:

• Jeg anvender min nye færdighed ... sounds slightly more formal
• Jeg bruger min nye færdighed ... sounds more natural in casual conversation

Both are grammatically correct.

Because færdighed is a common-gender noun in Danish.

Danish singular nouns are usually either:

• common gender → takes en, den, min
• neuter gender → takes et, det, mit

Since it is en færdighed, you get:

• min færdighed
• not mit færdighed

A good habit is to learn nouns together with their article:

• en færdighed
• en tekst

That makes it easier to choose min/mit, den/det, and adjective endings later.

Because after a possessive like min, the adjective usually takes the weak form, which is often -e.

So:

• en ny færdighed = an indefinite phrase
• min nye færdighed = with a possessive, so the adjective becomes nye

This is a very common pattern:

• en stor bil → min store bil
• et nyt hus → mit nye hus
• en dansk bog → min danske bog

So min nye færdighed is exactly what you would expect.

This is the normal Danish pattern for a definite noun with an adjective.

In Danish, when a noun is definite and has an adjective before it, you usually use:

• den/det/de + adjective + noun

So:

• teksten = the text
• den danske tekst = the Danish text

Notice that Danish does not normally say den danske teksten in standard usage. That would be wrong here.

Also, dansk tekst without den would mean something more like Danish text in a general or indefinite sense, not the Danish text.

Because tekst is also a common-gender noun: en tekst.

So the matching definite article is:

• den for common gender
• det for neuter

Compare:

• den danske tekst
• det danske ord

Again, learning nouns with en or et is the key.

Når is used for something that happens whenever or when in a general, repeated, or future-related sense.

Here, the sentence describes a general situation:

• I use my new skill when I translate the Danish text

That is not one single past event. It is a repeated or general action, so når is the right choice.

Use da for a specific event in the past:

• Da jeg oversatte teksten, brugte jeg min nye færdighed. = When I translated the text, I used my new skill.

A quick rule:

• når = when/whenever, general or repeated
• da = when, one specific past occasion

Because når jeg oversætter den danske tekst is a subordinate clause, and Danish subordinate clauses usually keep the order:

• conjunction + subject + verb

So:

• når jeg oversætter ...

That is the normal structure.

This is different from main clauses in Danish, where the verb often comes second:

• Jeg oversætter teksten.
• Nu oversætter jeg teksten.

But after når, you are inside a subordinate clause, so jeg comes before oversætter.

Because this clause needs a finite verb, not an infinitive.

• oversætter = present tense, finite verb
• oversætte = infinitive, like to translate

After når jeg ..., you need a full clause with a subject and a conjugated verb:

• når jeg oversætter ...

You would use the infinitive in different structures, such as:

• at oversætte teksten
• jeg vil oversætte teksten

So in this sentence, oversætter is correct.

Because the sentence expresses a general or habitual action.

• Jeg anvender ...
• når jeg oversætter ...

This means something like: this is what I do in that situation.

Danish often uses the present tense this way, just as English does:

• I use my new skill when I translate the Danish text.

It does not have to mean only right now. It can also describe a regular pattern.

Because når jeg oversætter den danske tekst is a subordinate clause, and many Danish writers place a comma before such clauses.

So the comma separates:

• main clause: Jeg anvender min nye færdighed
• subordinate clause: når jeg oversætter den danske tekst

You should also know that modern Danish allows two comma styles, so you may sometimes see:

• Jeg anvender min nye færdighed, når jeg oversætter den danske tekst.
• Jeg anvender min nye færdighed når jeg oversætter den danske tekst.

Both can be acceptable depending on the comma system being used.

In this sentence, den danske tekst will normally be understood as the Danish text, meaning the text in Danish.

With language-related nouns, dansk often works this way:

• en dansk tekst = a text in Danish / a Danish text
• et dansk ord = a Danish word
• en dansk sætning = a Danish sentence

Sometimes context could also suggest something culturally Danish, but here the most natural meaning is simply the text written in Danish.