Can a person sprain an ACL (not tear it)? If so, how many sprains before the ACL tears?

No. The definition of "sprain" is a rupture or tear. There are less commonly partial tears of the acl, but even partial tears are less stable and more easily ruptured. A "strain" is defined more as an injury without rupturing or tearing.
ACL sprain. The answer is yes. A sprain is due to a distracting force below what is required to actually rupture the ligament. There is no magic number for how many times it can be sprained before rupture. With each sprain the ligament becomes a little weaker; then it just depends how much force is applied against the ligament.