It's said as sk before the "hard" vowels a, o, u, å and as that other sound [ɧ] before the "soft" vowels e, i, y, ä, ö.
Some exceptions apply in loan word, e.g. skelett is said with an sk sound just like 'skeleton'.
skada (damage) = sk, because vowel (a) is 'hard'
skärgården (archipelago) = chw/soft sound like in loch, because vowel (ä) is soft.
What is the relationship between varlig and allvarlig? And an earlier exercise in this section had "mycket allvarlig" - so the "all" in itself doesn't already convey that meaning?
As stated by other, varlig is never used in modern swedish except in the song mentioned. But if you're interested, it means "careful" or "cautious".
I generally agree with the above posters, but it's actually in some use - you might encourage it in newspapers very rarely, but occasionally. It's practically never in use in speech, though.
Is "damages" (plural) the right translation here? As far as I know it means rather financial losses than a physical injury - that would be "damage" (singular). English isn't my native language, so I might be wrong through.
It depends on context. If the damages are separate, countable things, then the plural form should be used. If you're talking about a damaged object, then the damage isn't countable, and the singular form should be used. The same applies to financial damage -- if they're countable, then use damages.
In the sentence above, I have to say, 'injuries' is a much better translation than 'damage' (or 'damages').
Generally, I would say that even if the items in question are plural, we still use 'damage', when referring to physical damage. e.g. "there was lots of damage to our windows" - damage is being used similarly to 'mud' in the sentence "there was lots of mud on my trousers" or to the way 'milk' is used (as a substance rather than a countable item) "there is lots of milk in the buckets" (you would never say "there are lots of milks in the buckets"). 'Damages' is normally interpreted as a financial term, as you say.
So un Swedish skadar is both injuries and damages? In English , injuries are to people, damages are to things