Ladekabelen er ødelagt, så jeg lader telefonen med powerbanken.

Because Norwegian often uses the definite form when talking about a specific, known thing.

• en ladekabel = a charging cable (indefinite)
• ladekabelen = the charging cable (definite, masculine -en)

Also, ladekabel is a compound noun: lade (to charge) + kabel (cable).

Norwegian nouns have grammatical gender:

• masculine: -en in the definite singular (e.g., kabelen)
• feminine (optional in Bokmål for many words): -a (e.g., jenta)
• neuter: -et (e.g., huset)

kabel is typically treated as masculine, so you get kabelen → ladekabelen.

That’s a very common pattern: to be + past participle used like an adjective.

• er = present tense of å være (to be)
• ødelagt = past participle of å ødelegge (to ruin/break)

Here it functions like an adjective meaning broken/damaged. Similar idea to English is broken.

Sometimes, yes. Past participles used adjectivally can agree with the noun:

• common gender singular: ødelagt
• neuter singular: ødelagt (often the same here)
• plural: often ødelagte

Example:

• Telefonen er ødelagt. (singular)
• Telefonene er ødelagte. (plural)

In your sentence, ladekabelen is singular, so ødelagt is correct.

Because så here functions like so/therefore, linking two full clauses:

• Ladekabelen er ødelagt, (clause 1)
• så jeg lader telefonen ... (clause 2)

Norwegian normally uses a comma when connecting independent clauses with words like så, men, for, etc.

Both can exist, but they can feel slightly different depending on structure and style. Common patterns:

• ..., så jeg ... = very natural in speech/writing for consequence (..., so I ...)
• ..., så ... jeg ... (inversion) is also possible in some contexts, but så jeg is extremely common when så is acting like a conjunction.

If you instead use derfor (therefore), you typically get inversion:

• Ladekabelen er ødelagt, derfor lader jeg telefonen ...

lader is present tense of å lade (to charge). Conjugation is simple:

• infinitive: å lade
• present: lader
• past: ladet
• past participle: ladet

Norwegian verbs don’t change with the subject (no I charge / he charges difference), so jeg lader, han lader, de lader all use lader.

Because it’s typically understood as your/the phone you’re talking about (a specific phone). Norwegian often prefers the definite form in everyday situations where the object is identifiable from context:

• jeg lader telefonen = I’m charging my/the phone (context makes it clear)
  If you said jeg lader en telefon, it sounds like I’m charging a (random) phone.

med often means using / by means of:

• jeg lader telefonen med powerbanken = I charge the phone using the power bank

You may also see alternatives depending on nuance:

• jeg lader telefonen fra powerbanken = focuses on the source of power
• jeg lader telefonen med en powerbank = indefinite (using a power bank)

Loanwords commonly get normal Norwegian endings. powerbank is treated like a regular masculine noun:

• en powerbank = a power bank
• powerbanken = the power bank

In writing you’ll also encounter powerbank vs powerbanke in some usage, but powerbank / powerbanken is very common.

In Norwegian compounds, the main stress is usually on the first part:

• LA-de-ka-bel-en (main stress on LA)

That’s typical for compounds: LADE + kabel → LADEkabel.