Portrayed how?
Whitebeard Pirates literally went to WAR against the World Govt. We saw children in countries singing about how Whitebeard was a Monster in the lead up to Marineford.
Big Mom Pirates literally nuke entire Islands if Linlin wants sweets.
Whatever the Beast Pirates do, aren't even public knowledge because what they do is in isolation in Wano.
So what gives?
They are the crew of "ogres". Their top commanders are labelled after natural disasters. Momonosuke's idea on what pirates are is that of huge, vicious, violent men based on them. Jack entered Zou and pretty much erased half its country in an irrational rampage. In contrast, Whitebeard went to war because his golden rule was broken by the Government, but his crew wasn't murderous overall. Linlin is indeed dangerous when she wants stuff, but her country is seemingly peaceful and works like a more or less functional society leaded by a crime syndicate, not by barbarians. And Shanks chills unless you mess with a friend of his.
I don't know, I find it clear the Beasts Pirates are portrayed like, well, more beastly than other crews. It's in their theme.
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King is sole survivor of his race. And they dont know that Alber is King.
Thus they are offering a reward since they have no idea where Alber is.
Even if King truly is the only survivor of his race, the Government can't just assume he is. They know what kid they had in their laboratory, if he was their only concern they'd just be sending a bounty for his head just like they put a price for the only Ohara survivir, not just a vague 100 million reward for any information on Lunarians.
Again, they have no way to know whether King (who obviously is known to be a Lunarian by CP-0, therefore the Government, if Linlin knows, rumours exists and Marco inferred with half a thought) is the last of his race or not. If they found one Lunarian alive thirty years ago in spite of their purge happening around the Void Century, then it'd be stupid for them to not offer a reward for information on Lunarians overall, not King alone, just in case. It's common sense.
The reward isn't for King. Whether they know he's a Lunarian or not, they simply can't know for sure that Alber is the last one (if he truly is).