From what you describe she was very close to becoming someones dreadful furry hat. She was probably mishandled or abused. Chins take time to gain trust. If you push it and keep grabbing her and upsetting her, she may never come around. They have very good memories. She may never forget traumatic...
There isnt much choice. I use the same type small pet taxi. Sure they chew on it a bit but Ive never had a medical issue with any of my chins. Once they are in the car they usually dont care about that stuff. Only other option is a show carrier.
Eating poo is normal. Fur in poo, I have never seen. Check your chin out for any patches or fur missing or lighter fur in a certain area. Maybe shes chewing her fur somwhere and eating it. Thats the only thing I can think of as to why fur would be inside of her poo!
They will come around. What I recommend doing is letting them get used to being next to you. Try to keep them in room that you are near by, occasionally walk over and talk to them let them smell you. Eventually put your hands inside of the cage palms up and let them use you sort of like a tree...
I have come to find that the noise really depends on the cage. If you have a lot of stuff that is loose or spacious in the cage when your chin is running on his wheel, it will shake the cage therefore causing noise.
She definately wont drink from a bowl. I agree if you are using a different type of bottle, it may take her time to figure out what it is and how to work it. Try kinda showing her that water comes from there. It took a minute for my chins to learn how to get water from my edstrom bottles. Also...
The valve bottles with flip tops I have found to be the best. I use 2 edstrom water buddies. I recently found they stoped making them. Lixit has a similar one that has great reviews. Check amazon. As for the sheild guards, flower town chinchilla sells them for $7 or $8.
Just a thought.....Are you positive SHE isnt a HE? Strange substance is common with boys. If you catch my drift. My boys tend to make fleece items their "girlfriends"....
Trust me...go to the store and buy some shreaded wheat. Then go to your local vitamin store and buy some activated charcoal and acidophilas tablet (make sure you fridge them). Its not expensive. Your chin is very stressed out right now, kinda like if you have a stomach ache when you are scared...