He's also a reminder that there's light even in the darkest moments. Like Gildor and his elves showing up to scare of the Rider early on, and Rivendell later - but unlike the elves TB's presence is permanent. He's not going to fade and leave Middle-Earth to its fate.
He foreshadows that there's...
Probably because if you knight someone who brings dishonour to himself - most noticeably by not being a capable fighter - the dishonour would attach itself to you too. It's supposed to be an exclusive club, and the members won't take kindly to someone who lets any old riff-raff join.
As a cat person, I'm astonished at the idea of teaching a pet to modify its behaviour. The only thing I've ever known a cat to learn is to be more demanding and self-absorbed.
One where HR gets involved.
Done in the style of Andor, with complaints about HSE, demands for paid leave, better training for Stormtroopers, walkouts in protest about Vader's treatment of his officers, rumours about droids taking people's jobs...