Congratulations on your new bun!! She is super cute!
It is a bit unusual for buns to be very social and outgoing after just 2 days in a new home, but its not a sign of anything bad. The bun I have now needed 4-5 days, which is also a short time. It is lovely when a bun wants to be pet and hang out with their human!
Fearful rabbits tend to lunge or charge if they feel cornered and cant run away or hide, but there are the odd few that will attack. This primarily occurs if you do sth in the rabbit’s territory (“cage aggression”). Your girl doesn’t seem fearful.
Rabbits can however nip to get a point across, for example if you are in their way or if you have the audacity to stop petting them too soon 😃 When a rabbit nips as a means of communication, it can hurt because we dont have fur to protect us. It is however not an act of aggression. If you let out a squeak, it can help your bun understand when a nip is too hard.
Rabbits should produce lots of round poop, 200-300 per day for an adult medium sized bun. More poop is better than few poop. Moving to a new home can affect the stomach and the eating habits. Water consumption is also important for poop. Does she have a bowl or a bottle? Did she have a bowl or a bottle in her old home? Is she eating hay?