Is it possible to have good sperm motility but poor morphology? 12% morphology, 70% motility? was the test accurate with these figures?

Morphology likely OK: Sperm morphology (the proportion of sperm that are normally shaped) is measured in different ways. The best is called "strict" morphology, because it predicts fertilization efficiency. Using that method, 12% normal sperm is actually very good and well above the value associated with decreased fertility (4%). Check the normal range for your test. Your result is probably normal.