What kind of a name for a girl is "Wilhelm," anyway? A last name. Her full name is Sanaa Wilhelm. See the cast page for Volume VII. (And that's not even her REAL name. She dropped the family name because she didn't want to get heat in prison.)
Are the Jägermonsters really constructs? Why don't they have any stitching? There's more than one way to create a monster. Jägers are of the "drink this" variety (similar to Mr. Hyde). See also the (most excellent) article on how constructs might be categorized.
Klaus is a construct?! But he's a Spark! According to rumors, there were three sparky Wulfenbach brothers who were involved in a terrible lab accident. The current Klaus was constructed from the remains of the three.SB Whatever the circumstances, the authors have stated more than once that, yes, Klaus is really a construct.
What is the status of religion in Europa? We don't know, although "7 Popes" have been mentioned and one of the old Heterodynes was called a blasphemer, implying that there was something to blaspheme in the first place. Though in a universe ruled by science gone mad, who knows what any of that means? (Feel free to debate on the Fan Theories forum.)
Has anyone noticed that in the time portals, Agatha's sigil has wings? Does this signify a Wulfenbach-Heterodyne alliance? We've noticed, but we don't know for sure. In spite of this meme getting around, we don't know for certain if wings are unique to Wulfenbach or what the significance is.
What's the deal with the face on Zeetha's headband? It changes! Yep, and it matches her expression, too! Originally thought to be merely an amusing sight gag, Zeetha later gives it to Higgs, using its psychic connection to herself to help maintain their long-distance relationship.
________ appears to have fangs. Is he/she a Jäger? Not necessarily. When characters feel fierce, or especially angry or vicious, their teeth get a little sharper, in the same way that surprise will make a character's hair stand on end. These are just trademarks of the Professor's drawing style.
What's the significance of "2 years and 3 months" on this page✣ ? Carson is just being very precise as he explains why Klaus could not possibly have been the father of Klaus Barry Heterodyne. Apparently this was a rumor both within the Girl Genius universe and ours, in spite of the math. Of course, when time travel might be involved...
Are Gil and Agatha siblings/half-siblings/second cousins/ex-roommates/related in any way, shape or form? No. Most emphatically no. The Professori have gone on record to say that there is no Luke/Leia thing going on here.
What is the function of Othar's visor? None is known other than the obvious one of creating a barrier between Othar's eyes and the rest of the world.