Ya, I think its possible for fans to interpret that perhaps Malicia was behind both kidnappings (somehow). I think its similar to how people have interpreted that most, if not all of the KQ villains are members of the Society of the Black Cloak in fan fiction and fan games. However, in reality the Society of the Black Cloak was limited to being an idea of Jane Jenson's, that wasn't seen important to Roberta Williams. Roberta has admitted she knew very little bit about the idea, and never thought of using it later.
However, as far as I know none of the original background documents ever actually implies that Malicia was connected to the original kidnapping. The few references in the game, and the more detailed backstory documents in the official strategy guide and companion, never actually specifically ties Malicia to the first kidnapping.
Actually more than anything, it seems the royal family of Etheria, does a good job of pissing off their subjects in some way, making some of them want to get back at them by attacking that which they held the most dear (in which case Edgar becomes their target).
I don't recall Lolotte's reasoning for the kidnapping exactly, as it was revealed in the backstory documents, but as I remember; it had less to do with her wanting to personally take over the kingdom (although she might have tried). As I recall it explains that had a bad attitude (and was misusing her powers), she was banished by the royal family for it. So to get back at them she snuck back into Etheria, kidnapped Edgar and ran away to Tamir.
Oh, and Genesta isn't connected to Etheria - she has wings.
Ya, as for Genesta. Ya she has no connection to Etheria in any of the material. She has always been desribed as being "queen of all fairies" and the Queen of Tamir.
That would put her in a position of power equal to Titania who was queen of all fairies in Etheria or Ahi'aorina Culatha Alimehenii who was queen of all fairies in Daventry (KQ novels).