Since "sjanse" is masculine, shouldn't it be "den var vår siste sjanse"?
"Det" is used to introduce nouns no matter what their gender/number is.
"Det er bøkene mine." (Det means bøkene)
"Det er boka mi." (Det means boka, feminine noun)
"Det er Eriks bil." (Det means bil, masculine noun)
When it is already introduced however, the pronoun is changed to fit the noun: "Det er Eriks bil. Den er fin."
Still do not get why it is "siste" but not "sist". I'm pretty sure I've met the phrase "sist gang" here. In both cases the nouns are masculine. So what are the rules for the adjective "sist-sist-siste" then?
I believe this is because "sjanse" here is in the genitive case (the chance belongs to us), which means that any adjective must take the "-e" form.
The correct answer was in the "Adjectives"-"Combining possessive pronouns with adjectives" section. I just forgot the 2nd part of it. You have 2 ways of combining a possessive pronoun with an adjective:
Det var den siste sjansen vår
Det var vår siste sjanse
While adjectives without possessive (just for comparison):
Det var den siste sjansen
Det var en sist sjanse
In both cases with possessive pronoun the adjective goes with -e ending as if the noun was in the definite form.
Why is there a "g"? I know in Icelandic you and sound like CH or H before some double consonants (e.g. ekki), but never heard about anything like this in Norwegian.
It's not standard Norwegian ortography, but rather a loanword which has been adapted into the language from Latin via French. The sound that's used when pronouncing it in French does not exist in Norwegian, and this "ng" sound is the substitute.
You'll see this tendency when it comes to most of the French loanwords ending in -ent, -ant, and -anse.