My rabbit Dobby is allergic to pine so I use the Oxbow eco straw pellets instead. I think for rabbits I find oxbow is better versus the pine pellets that we have in my area. I find the pine pellets to be a bit sharper and even in pellet form he wont use them. Our other rabbit Castiel is okay...
Not sure I can help with the breed, but based on the rabbits we have at home, I almost think they look like a rex mix? With the weights you gave I think mini rex possibly. My daughter has a Mini Rex and he is the softest thing you will ever pet so if the fur is super soft that could be another...
I know this may sound strange but do you use pine shavings for bedding? I have a lion head bunny who is terribly allergic so I had to switch to something different. I found oxbow eco-straw works great. It is a wheat based pellet that if eaten is digestible. Good Luck and I hope Betty feels...