4-year-old with tingling in feet, low back pain (mid-left), yellow stool (sometimes pale), and nighttime nosebleeds. What tests should I request?

Just take. Your child to the doctor, the doctor will know what to do from there.
History & Physical. Symptoms you are describing don't easily fit together. Before jumping to tests a thorough history and complete physical exam will help lead your doctor into ordering the appropriate studies.