I am not certain by any means, nor do I have an exhaustive knowledge of the powers of Satan. I know that Satan has more power than one would normally find among human beings. At the same time, I know that Satan is not divine; he is not God, does not have divine powers or attributes. He is a creature with the limitations that are found normally with creatureliness. He is an angel.
The Bible doesn’t give us an exhaustive list of the powers of angels. They are more powerful than people but far less powerful than God. Obviously God can read your mind. God is omniscient. He knows your thoughts as you think them—“There is not a word on my tongue, but behold, O Lord, You know it altogether” (Ps. 139:4). The tendency is for Christians to think that since God is a supernatural being and can read our minds, then Satan, also a supernatural being, must be able to read minds, too. But Satan’s powers are not equal to God's.
A similar question would be, Can Satan be at more than one place at a time? I would be inclined to say no. I doubt that in my lifetime I will ever have to worry about Satan reading my mind, because I will probably never meet him. He can only be in one place at one time. He’s a creature, and creatures by definition are limited spatially and temporally. So Satan cannot be at more than one place at a time. He has all his little junior assistants, and he might send one of them to harass me and to tempt you and accuse you, but he’s going to save his time and energy for people of greater influence than me.
Satan focused his assaults upon Jesus in the New Testament. In the Temptation he entered into dialogue with Jesus. He knew what Jesus was thinking because of what Jesus said. But other than that, I dont see any reason to believe that he could read your mind or read mine. Again, that may not necessarily be a divine power. He may be able to do it, but I have no reason to believe that he can.