Do minor tendon tears recover and repair?

Yes they do. Minor tendons tears heal if you protect them during the time of healing, some times if the tear is not complete the tendon will heal and there is for surgery if you do not they may go on and rupture in this case you need a repair.
It depends. If the tendon is torn away from the bone, then it will not heal. If the tendon is partially torn in the mid-substance, it should heal. Even tears that don't heal may stop being painful.