Is there a permanent cure for si joint dysfunction?

No. There is currently no "cure" for si joint dysfunction. This condition is usually best treated with aggressive physical therapy to stabilize the pelvis, restore normal alignment, and strengthen the core. Medication, injections, braces, and modalities (heat/ice/etc) may also be used to reduce pain during this process.
No. Once it occurs, it can come back. It is important to learn how to do the home exercises to self treat recurrences.
No. The sacro-iliac joint or s-i joint is a very unusual true source of pain. It is much more likely that pain in the region of the s-i joint is related to the lower back. Physical therapy is the mainstay of treatment.