1) Technically your doctor is wrong or you misunderstood; absence of WBC in
urine does not rule out gonorrhea or chlamydia. However, as just
explained, if your STD risk is low, then testing may not be necessary.
2,3) This sounds like you are describing the dipstick results for urinalysis. They often are weakly positive if the urine is quite concentrated -- for example, if you had not been taking in lots of fluids in the hours before testing.