Hii CONGRATZ ON YOUR BUNNY!! Now as for the rabbit not running around as much its not something to worry about, she is probably getting used to her new environment. Is she eating,sleeping and drinking regularly?
Litter box training, I just trained my lola how to used the litter box
! Its great to have a rabbit litter box trained. Anyway to start off you need to have a square shape litter box big enough for her to sit in it comfortably, the corner type ones are not as good as the square my bunny in fact never used her corner litter box. Also it would be a great idea to take out all the shavings in the cage and just have a bare bottom cage so its not as confusing to have litter everywhere just have the shavings in the litter box. Its also a good Idea to have hay in her litter box because rabbits tead to go potty where they eat. Is your bunny spayed? If not it would be a great idea to have her so because it will be a lot easier to train her
Toy~ you can use anything as a toy for her, like the tube for the toilet paper, cat toys, bird toys really anything that catches your bunnies eyes. Mine loves to play with some cat toy balls I got her. She throws it around in her cage and out on the floor where she is running about. TREATS YUM
Mine Loves carrots and lettuce. Now I wouldnt recommend those treats you find in the pet stores that have tons of sugar in it. The treats that looks like you would even eat it, those can cause cavities and tooth decay.
OH Yea and when your bunny has her litter training like a pro you can add a small dog bed in her cage, she will love it! As for her ear flopping o.0 I dont know anything about that sorry, when I got my Lola her ears were already flopped she was about 10 weeks old when i got her