If you consider Wolves as dogs then yes. In episode 5 after Jonas betrays Anna. He sends a pack of wolves after her and Shall. In self defence Shall kills many of them
Only side characters die, not main
Even in the light novel where Mythril Lid Pod is bound to pass away because he's a water fairy and where Anne gets severely injured they're still alive at the end of the light novels
Episode 11, briefly mentioned as a worldbuilding tidbit
(Paraphrased) "God intended humans to rule the world, but a human woman fell in love with the fairy king. King Cedric then had to act to rinse of this sin."
Not kidnapped, but held hostage
Episode 21 onwards, main character is abducted from her crafting guild and is forced to make sugar candy for the rebel fairy leader, this is to get the love interest to follow him around and potentially have him as an ally
*Spoilers* episode 7 Jonas Anders (probably the same age as Anne, 15) is seen with a bruise on his cheek, episode 8 reveals it's from Duke of Duke of Philax/William Alburn and the duke wants to hit Jonas again for asking to leave because he wants to quit