Can a drug test tell how long ago and how much of the drug you took?

Not generally: Some drug tests simply give a yes or no answer. However, when a drug test quantifies the amount detected in the blood or urine, it's often possible to estimate how long ago a known dosage was taken, or, conversely, the dosage given knowledge of how long ago it was taken. I.E., if you know one, it's sometimes possible to estimate the other.