You don’t seem like an incompetent owner, of course.

Some rabbits are more fearful than others, fearfulness is a trait with strong heritability. I can’t say what’s up with your bun, but being alone for 9 hours every day is perhaps not ideal for him. Licking can be a display of affection or a request for grooming, but it can also be a signal of appeasement. Like look I’m nice, please be kind to me. My Bam displayed that type of licking when I first got him – he didn’t know me, so he didn’t have any reason to be affectionate towards me.

I think perhaps you should try and relax and not try so hard. You are used to other animals, and maybe that’s making you a little bit impatient with yourself. He has everything he needs. Now he needs time to settle. You could perhaps leave the tv or a radio on for him while you are gone during the day, on low volume. Buns never wear their hearts on their sleeves, if they did, that’d be the last thing they’d ever wear, so to speak.

You don’t seem incompetent – you have to learn somehow.

I have found the best way to get new and nervous buns used to me is to sit down in the same room as them and mind my own business. So I bring in my laptop or a notebook or a book – something to do. And I let the bun mind it’s own business around me. It’s a great way for them to get used to my presence without me doing much.

I find the best place to start patting is the centre of the nose, and I stop if the rabbit backs off. So I let the rabbit approach me, and I offer a pat by holding my hand gently near the nose. If the rabbit doesn’t back off, I pat. If the rabbit backs up I move my hand away. Once I can do the nose I work my way around to find out what else the bun likes – often between the ears is a good next step. Sometimes the cheeks, sometimes behind the ears, the shoulders, or even the ears themselves.

I found Terry started to warm to me a lot when I ate (or pretended to eat) veggies near him. He decided he wanted what I was eating so I would offer it to him and he would gobble it up near me.

I agree with Bam – try to relax. If you are upset or stressed around horses the horse will pick up on that. It’s the same with rabbits, just not always as obvious because you don’t have 500+ kilos of flight animal having a dummy spit on the other end of a relatively short rope. Sitting and minding your own business around bun will help you with that.

Could you put blankets or rugs on the carpet? When my bunny chews on carpet I put down blankets and he usually stops. (He’s a weirdo).
It’s sounds like your a good bunny owner
You’re doing your best to make him happy. It can take a long time time for bunny’s to really warm up to you. It took my bunny around 8 months and about 4 of those I spent almost everyday hanging out with him all day. I don’t think most buns take that long at all but don’t be discouraged. And he lets you pet him sometimes that’s good
And if he’s a baby/teenager your probably going to have bar biting. Just means he wants out.
Don’t feel frustrated though dogs and horses aren’t really like rabbits. The knowledge you have with them sometimes is going to be the opposite with bunny’s behavior wise. Not always. But yeah.
Oh. Does your bunny have a place to hide in his cage? You could even drape a blanket over half of it. Sometimes that helps them because then they have a little safe spot.
Good luck with your bun