Hi Ella and welcome to the nice bunny world! I’m also a new dad, only 2 weeks in, but from my experience and what I’ve seen on the web I can give you a few advice!
For the litter training, I suggest you to put her hay rack and hay inside the litter box. Since it’s a cat litter I don’t know if you’ll be able to hang a hay bag but that’s the best advice, bunnies basically eat hay and dump it right away …
For bonding with your bunny, I suggest you leave her a little time. From what I’ve seen with my Maui, they need time to adjust to you but also to the environment. New sound, new smell, etc. They have a gland under their chin and by rubbing it on surface they kinda make it their own and remember the place is safe.
Also, even though I was not the best at it, I suggest you hang outside her pen for the first 1-2 days. If she’s curious and come see you, you can maybe go inside the pen and listen to your course witouth trying to touch her. She has to know that your safe and that she can trust you.
Don’t be hard on yourself, I was and still am a bit but bonding takes time, could go from days to a few months, but since you seem like you’re going to take the time, you’ll have a nice relationship I’m sure.
Don’t try to pick her up, I do it cause I have no choice for medicine, but I’d build trust with my bunny before training for picking up. Instead you can teach her her name, or tricks. Treats is always the best. They say treats everywhere on internet but pellets and vegetables work just as well 🙂
Once you’ve spend maybe 1-2 days going to her pen, you can try to hand feed her, no petting, she’ll learn to trust your hand and the feeling of them.
As for petting, I think every bunny is different, I’m trying to understand when my bunny wants it. I found that when he kicks my face, or is sleeping next to me, or when he come and lower is head (that’s bunny langage), that’s when I can let him.
Mine grind his teeth when he likes it that an indicator! Don’t rub his belly, under his chin or tail, they hate that !
Finally try to have a routine, bunny are very routine oriented, they’ll know that it’s time to eat in the morning, and at noon 🙂
There you go, if you have any other question let me know !