Hi! What you can sew through is going to depend on your machine. I started sewing about 2 years ago and I've gone through 3 machines - not broken them, but just kind of out grew their power. My new Bernina can sew through practically anything. Make sure you are using appropriate needles (denim, leather, etc.) and keep your machine oiled. I've never sewn with fur, but if it's like Minky, I think the appropriate needle would be a universal or ballpoint because it is knitted (as opposed to woven cotton - I use 'sharp' Microtex needles for cotton) And those are not going to be as sharp. You could always use a bigger needle though. Someone with more experience with this type of fabric will have more answers, I just wanted to give you a heads up about it. I also use something called Sewer's Aid on my needles.
As far as the fur, the biggest problem I see is not being able to iron it. You need to massively interface the sophia bag to get it to stand up. What I would do, if you really want to try it, is use a layer of muslin under the fur, interface the muslin and then baste that to the fur. This is going to add extra layers, but it's important to use the stiff interfacing to get the shape of the bag.
You can use a zipper foot to do the piping. If you are using the fur, I don't think a piping foot is going to help you much because it's all going to be too thick to send under the foot anyway. Piping foots are most helpful when you are making lots of piping, which you won't be.
I hope that helps a little

Erin