JOEL - Satan created nothing. God created everything, even the little microbes that infect our bodies and cause illness. Diseases, including physical, mental, and emotional, are mostly caused by defects in our mortal bodies and the results of living with other mortals on this earth which God made.
There is opposition in all things(eg. good health and sickness)(2 Ne. 2: 11) Without the bad we cannot appreciate the good. Besides this, God allows disease to happen in our bodies to give us experience; to make us humble; to strengthen our character, and so that His works may be made manifest in us. (John 9:1-3)
Satan can take advantage of such conditions and take over our souls if we lose faith and allow these things to affect our spiritual health.
But Satan is rarely the direct cause of such things. His main job and goal is to tempt people to commit sin. God has told us that Satan has no power over children (D&C 29: 47), yet children do suffer from all kinds of diseases; so it can't all be caused by Satan.
Satan can tempt us to commit sin which can, if we give in to it, ultimately make us physically sick or emotionally depressed.
I think Satan's power can be involved in affecting some depression and even some madness in people who allow him inside(Matt 8:28-32).
President Ezra Taft Benson said:
"As the showdown between good and evil approaches with its accompanying trials and tribulations, Satan is increasingly striving to overcome the Saints with despair, discouragement, despondency, and depression." ( “Do Not Despair,” Ensign, Oct. 1986, 2).
But there are of course other types of depression and mental illness that are of a clinical nature that are caused by some genetically inherited defect or chemical imbalance in our bodies.
When the Lord placed enmity between Eve’s children and the devil, Satan was told that he would bruise the heel of Eve’s seed, but her seed would bruise his head. (See Moses 4:21.) So Satan can torment man in many ways, mostly by tempting us to sin, but most of the diseases and illnesses we get are simply an occupational hazzard, so to speak, because we live on this earth with mortal bodies.