Har du fått installert den nye appen, eller trenger du ladekabelen min?

Because it’s a yes/no question, Norwegian normally uses verb-first word order: Har (the verb) comes first, then the subject du.
Compare:

• Statement: Du har fått installert den nye appen.
• Question: Har du fått installert den nye appen?

It’s the present perfect (har fått) plus a past participle (installert) in a construction with få meaning roughly get/managed to get something done.

So har du fått installert X often means:

• Have you managed to install X?
• Have you gotten X installed? (by yourself or with help)

It focuses on the result being achieved, not just the action.

Yes, Har du installert den nye appen? is totally natural and simply asks whether you installed it.

Har du fått installert den nye appen? adds a nuance of:

• it might have been a bit difficult
• or you might have needed help
• and the key point is whether it’s now successfully installed

So fått installert can sound a little more like Did you manage to get it installed?

Installere is a verb in -ere, and its past participle is typically -ert:

• å installere → installert
• å reparere → reparert
• å organisere → organisert

Here, installert is a past participle used after fått.

That’s the common Norwegian pattern sometimes called double definiteness.

When a noun is definite and has an adjective, you normally get: 1) a definite determiner: den / det / de
2) the adjective in definite form: nye
3) the noun in definite form: appen

So: den nye appen = the new app.

Because with den + adjective + definite noun, the adjective takes the definite form, which for many adjectives is -e:

• en ny app = a new app
• den nye appen = the new app

So nye matches the definite structure.

Both are possible, but they differ in what sounds most natural and what they emphasize.

• ladekabelen min (very common) = my charging cable
  This uses a definite noun (ladekabelen) + possessive after it.
• min ladekabel = also my charging cable, but it can feel a bit more emphatic/contrastive (as in my cable, not someone else’s), and it’s less common in everyday neutral phrasing.

Norwegian often prefers the post-posed possessive: tingen min, bilen din, huset vårt.

It depends on gender and number:

• Common gender singular (en-words): min
  ladekabelen comes from en ladekabel → min ladekabel / ladekabelen min
• Neuter singular (et-words): mitt
  et hus → huset mitt
• Plural: mine
  bøker → bøkene mine

Since ladekabel is common gender (en ladekabel), it takes min.

The sentence is basically two coordinated yes/no questions joined by eller:

• Har du fått installert den nye appen, eller trenger du ladekabelen min?

Both parts are questions, so both use verb-first word order:

• Har du ... ?
• Trenger du ... ?

The comma before eller helps show the split between the two alternatives.

A few common ones:

• fått: the å is like an English aw-type sound (varies by dialect), and the tt is a crisp t sound. Many learners under-pronounce the final consonant.
• trenger: the ng is usually a single ŋ sound (like the end of sing), not n + g.
• ladekabelen: typically stressed early: LA-de-ka-be-len (stress patterns can vary a bit), and the final -en is a short, unstressed ending.