Hello,
This is usually painful bc the broken nai is irritating the sensitive quick underneath it. So removing the nail often alleviates the discomfort. But removing the nail is also painful which is why I use an analgesic or numbing agent. I use lidocaine gel. I also use a sterile blade or nail trimmers. I also use a medical antibiotic cleaner and oral antibiotic as I have seen a dog get tetanus after this.
Hello,
You can bring a fecal sample to your vet. They should be able to help.