Does having a ACL problem cause you to have slipping in the knee and instability?

Yes. An acl tear can result in knee instability. The lower leg (tibia) can slide forward and rotate relative to the thigh (femur). This can result in near dislocation events and can lead to further damage of the cartilage and meniscus. In younger patients who want to remain active in sports, a torn acl should be reconstructed by an orthopaedic surgeon.
Yes it can. If you have a complete tear in the anterior cruciate ligament you may feel as though your knee is slipping of shifting due to the lack of stability from that ligament. The stabillity of the other knee ligaments and quad and hamstring stability determine the amount of instability.
Yes. Acl functions to stabilize the forward backward motion of the knee (upper leg to lower leg) thus a tear can result in instability in that plane of movement. The decision for repair depends on several issues but primarily on your age, health and activity level.
Yes. A torn ACL can lead to knee instability. With each episode of instability, you run the risk of doing further damage to the joint, specifically meniscus/cartilage tears. This can lead to arthritis at a later age. See a knee orthopedic sports medicine surgeon, for the correct treatment.