Vi burde ha kjøpt en lengre forlengelseskabel, for stikkontakten er for langt unna.

Burde + ha + past participle expresses a past obligation/expectation that wasn’t fulfilled: “we should have bought (but didn’t).”
If you say Vi burde kjøpe ..., that usually means “we should buy ...” (advice about now/future).

Burde is a modal verb (past form of bør). It doesn’t take å before the next verb, so you say burde ha kjøpt, not burde å ha kjøpt.

After ha, Norwegian uses the past participle, not the simple past.

• å kjøpe → past participle kjøpt
• Simple past would be Vi kjøpte ... (“We bought ...”), which is a statement of what happened, not an unrealized “should have.”

The comparative of many short adjectives is formed with -re, not -ere.

• lang → lengre (comparative)
  Lengere is not standard Bokmål.

Both relate to lang, but they’re used differently:

• lengre = comparative adjective (modifies a noun): en lengre kabel
• lenger = comparative adverb (modifies a verb/phrase): kabelen rekker lenger (“reaches further”)

Stikkontakten means “the socket/outlet,” referring to a specific one in the situation (the one you’re trying to reach). Norwegian often uses the definite form when something is identifiable from context.

They’re two different uses: 1) for as a conjunction meaning because/for: ..., for stikkontakten ...
2) for as an adverb meaning too (excessively): er for langt unna = “is too far away”

Often yes, but it changes word order:

• ..., for stikkontakten er for langt unna. (main-clause order after for)
• ... fordi stikkontakten er for langt unna. (also common)
  If you start the sentence with fordi-clause, you get inversion in the main clause: Fordi ... , burde vi ...

Unna and vekk both relate to “away,” but they’re not identical:

• (for) langt unna is very common for physical distance: “(too) far away”
• vekk often emphasizes being “gone/away” or movement away.
  In this sentence, for langt unna is the most natural.

Unna functions like an adverb describing location/distance, and it pairs naturally with langt: langt unna (“far away”).

In expressions like langt unna, langt is used adverbially (“far”), and Norwegian typically uses the neuter form for many adverb-like uses of adjectives:

• en lang kabel (adjective with a noun)
• langt unna (adverbial “far away”)

Yes—Norwegian frequently makes compounds as a single word.
forlengelses- + kabel = “extension cable”

• forlenge = “to extend/lengthen”
• forlengelse = “extension”
• forlengelses- = linking form used in compounds
  So en forlengelseskabel = “an extension cable.”