Based on the dynamic, Caine likely finds Grace's defiance both irritating and intriguing. Her sarcasm challenges his authority in ways other wolves wouldn't dare, making her uniquely compelling to a King accustomed to submission.

No. Importantly, this is NOT a rejection romance. Caine never formally rejects Grace. Instead, it's a reluctant mates dynamic where both parties resist the bond for different reasons—Caine because she's human, Grace because he killed her pack.
Grace's ex failing to greet the Lycan King at his territory border is a grave insult in wolf society. It may indicate defiance, ignorance, or cowardice—all of which would provoke Caine's wrath.
Though specific physical descriptions vary throughout, readers note that Caine is described as physically imposing—rippling muscles, heaving chest (Ch. 149), powerful presence. Grace internally acknowledges his attractiveness despite her fear.
The quote about stabilizing her lifespan strongly suggests yes. The claiming/mating process may infuse Grace with supernatural vitality, potentially giving her a lifespan closer to that of a Lycan—an enormous incentive beyond romance.
By Chapter 219, it's become blatantly obvious to nearly everyone—including the Lycans, who "are not the brightest"—that Grace is Caine's mate. Only the stubborn parties (primarily Caine and Grace themselves) continue denying it.
Extremely. Chapter 37 ("Caine: You Touched Her") shows his violent reaction when anyone touches Grace. He also tracks her when she runs (Chapter 41), sneaks into her room (Chapter 221), and maintains constant surveillance.
The chapter describes Grace as "oblivious" with the fan blowing hair across her nose while she sleeps. This suggests she doesn't know about Caine's nocturnal visits, though she may suspect given his behavior changes.
Caine uses his Lycan senses to track Grace's scent trail. In Chapter 41, he pauses at her door to inhale the fading scent, then follows it. His supernatural tracking abilities make it extremely difficult for a human to hide.
Yes, multiple times. Chapter 41 shows Caine tracking Grace after she's been gone for two days. Her attempts to flee are driven by her desire for freedom and her horror at being bonded to the man who killed her pack.
Grace forces Caine to confront the limitations of pure power. Her moral objections, her courage despite weakness, and her ability to form bonds of loyalty challenge his "might makes right" philosophy.