The surface impression we get of the world of Girl Genius is that the Heterodyne Boys and Dr Beetle are heroes -- it says so right on the cards! -- and that Baron Wulfenbach is a villain -- everyone believes it! And it says so right on the card! And the Jagermonster says he'll break his own son down for parts!
Contemplation, however, has raised many doubts in my mind. The background notes themselves make the point that Wulfenbach does not retaliate for nasty things said about him, although this could easily be "I feel guilty" or "I don't care what you think" instead of "I believe in free speech".
But Dr. Beetle's card has, under the bold word "Hero", a rather creepy depiction of his bell jars and the various criminals -- murderers? Pickpockets? -- condemned to die in them. So my first thought was to wonder what "Hero" and "Villain" mean -- are they words describing actual deeds and atittudes on a scale of modern 21st century morality, or a scale of 16th century European morality, or do they simply reflect popular perception within the world? Certainly Beetle is seen as a hero, and Wulfenbach as a villain. By our standards, Beetle is at best a mix of enlightened despot and hideous criminal against humanity, and Klaus is UN KFOR.
So, what facts do we have? Beetle is a Tyrant, beloved by his people, who has Merlot do the unpleasant work, and throws criminals into bell jars to die, slowly. Wulfenbach comes from a minor house described as actually caring for its people; he spent his youth heroing with the Heterodyne Boys, was gone for a while, and is currently ending the War of the Sparks through the method of stomping on anyone who gets out of line -- less idealistic than the Heterodyne Boys, although possibly more effective, and less ruthless than the Other, who just killed everyone.
The Jagermonster says Klaus will have Gil broken down for parts if Gil fails his tests. But we also know "rumors" of that have reached Gil's ears... and that the Jagermonsters were made by a villain, and regret not working for one now. And what I've seen of their personalities does not make me think they have an instinctive regard for the truth... as opposed to, say, making up villainous stories about their current master to improve his reputation (in their eyes) and make themselves feel better.
I think it is safe to believe that the Heterodyne Boys were idealistic crusaders for Good; I won't be so cynical as to seriously entertain the idea that they invented marketing more than heroing. I will, however, suggest that mad scientist idealistic Crusaders for Good and Defenders of Humanity are still capable of being thoughtless, incompetent, or even petty and cruel, in dealing with people as individuals, in their personal lives. It is possible that Klaus left the gang not because he had to go nurse a wounded ego, but because Bill and Lucrezia were jerks to him... we should keep our minds open.
So, here's my guess as to Klaus's motivations:
He believes in noblesse oblige: with great power comes great responsibility. He also believes, from observation, that most people are barely capable of handling the responsibility of running their own lives, let alone having any power over others, or the power of the Spark. These beliefs, reached after an earlier idealistic stage, would largely explain his "very bad mood".
His tests of Gil are not primarily about testing Gil's mind or Spark, which should have been demonstrated fairly well by now. That's the cover. Klaus's real concern is with Gil's character, about whether he has the necessary combination of ruthlessness, decency, and good judgement to be allowed power. Possibly Klaus would be shocked at the idea that he'd kill his son. Possibly not -- but in the latter case, we should think about what it'd be like for everyone else if a Wulfenbach-level Spark was released upon Europe without good judgement and moral restraints.
I would guess that Adam and Lilith's fear of the Baron is inflated. If he learns that Agatha is a Heterodyne, he'll just take her in and educate her, subject to Gil's constraints (ill-behaved Sparks cannot be allowed to roam freely, for the good of the people.) I won't bother trying to guess what's between him and Barry.