Learn Russian: Они не могут идти в музей, потому что работают. - They cannot go to the museum because they are working.

No. In Russian, почему is strictly a question word meaning "why". When you want to say "because" to give a reason, you must use потому что, just like in this sentence.

Is the comma before потому что required?

Yes! In Russian, you must always put a comma before joining words like потому что (because), что (that), and но (but) when they connect two parts of a sentence.

Why does the sentence use идти (to walk/go) instead of ехать (to ride/drive)?

Using идти implies they were planning to go to the museum on foot or that it is located within the same general area. If they were planning to travel by car, bus, or train, the sentence would use ехать.

Why doesn't the word музей change its ending here? Doesn't the Accusative case usually change endings for destinations?

You are right that going to a destination requires the Accusative case. However, for masculine inanimate objects (things and places, not people or animals) like музей, the Accusative form is exactly the same as the standard dictionary form.

Why is there no они (they) before работают (are working)?