Spillbrikken kan være blå, eller grønn for den saks skyld.

Because Norwegian usually writes compound nouns as a single word.

• spill = game
• brikke = piece / token / tile

So spillbrikke means game piece or playing piece, and spillbrikken is that same noun in a definite form. English often uses two words where Norwegian prefers one compound.

The ending -en marks the noun as definite singular for a common-gender noun.

So:

• en spillbrikke = a game piece
• spillbrikken = the game piece

Norwegian often adds definiteness to the end of the noun instead of using a separate word like the.

Because after a modal verb like kan, Norwegian normally uses the infinitive without å.

So:

• kan være = correct
• kan å være = not correct here

This is the same pattern you see in:

• jeg kan svømme = I can swim
• du må gå = you must go
• vi vil spise = we want to eat

In this sentence, kan means something like can / may / is able to / is allowed to, depending on context.

Here kan most naturally expresses possibility or allowed options.

So the sentence is not saying the piece is blue. It says that blue is one possible color, and green is another possible color.

Compare:

• Spillbrikken er blå. = The game piece is blue.
• Spillbrikken kan være blå. = The game piece can be blue / may be blue.

They are predicate adjectives, because they come after være.

In Norwegian, predicate adjectives agree with the noun in gender and number. Since spillbrikken is singular common gender, the forms are:

• blå
• grønn

If the noun were neuter, the forms would change:

• et hus kan være blått
• et hus kan være grønt

So grønn is used because spillbrikken is not neuter. Blå already has the correct form here as well.

It is a fixed idiomatic expression meaning something like:

• for that matter
• if it comes to that
• for all I care, in some contexts

In this sentence, it makes grønn sound like an added afterthought:

• It can be blue — or green, for that matter.

So the speaker first mentions blue, then adds green as another perfectly acceptable possibility.

Yes, but in practice you should learn for den saks skyld as a whole expression.

• den = that
• skyld often relates to sake, and in other contexts can also mean fault
• sak means matter / case / issue

But in this sentence, you should not translate it word-for-word. The whole phrase functions idiomatically as for that matter.

Because eller introduces an alternative: blue, or green.

But with for den saks skyld, it does more than just give a neutral list. It gives the second option an afterthought feeling:

• first idea: blue
• added thought: or green, for that matter

So it sounds a little more conversational than a plain list.

Usually, no. In standard Norwegian, you would often write this without the comma:

• Spillbrikken kan være blå eller grønn for den saks skyld.

The comma in your sentence mainly creates a pause before the afterthought. So it may be stylistic, but it is not normally required.

No, it is mostly standard Norwegian main-clause word order:

• Spillbrikken = subject
• kan = finite verb
• være = infinitive
• blå = predicate adjective
• eller grønn for den saks skyld = alternative/additional phrase

So the basic structure is:

subject + finite verb + infinitive + complement

This is very normal in Norwegian. The finite verb kan appears early in the clause, as you would expect in a main sentence.