The Bible does teach us that Satan indeed is very powerful. Likely he was the highest ranking of all the fallen angels, as he was persuasive enough to convince one third of the angels to join him in his rebellion (Revelation 12:4). Even after his fall from heaven, not even Michael the archangel dared to confront him without the Lord's help (Jude 1:9).
Satan is the "the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient" (Ephesians 2:2b).
Believers are exhorted "Resist the devil, and he will flee from you" (James 4:7b).
Now to answer the crucial question:
Can Satan and/or his demons read our minds?
Scripture does not say specifically whether or not Satan can read our minds. First, it is important for us to remember that Satan is not omnipresent; he cannot be in more than one place at a time. Only God is everywhere, only God knows everything, while Satan must rely on his army of demons to do his bidding. The Bible gives us no reason to believe Satan and his demons can read our minds. Clearly that would take a measure of omnipresence and omniscience, which they do not have.
However, Satan and his demons have been observing and tempting human beings for thousands of years. In addition, they can overhear our speech when we talk to others (and to ourselves!). Surely they have learned a few things about us over the years. Even without the ability to know our thoughts, they can probably make a well-educated guess as to what we are thinking, and then attempt to use it to their advantage. That is why we are commanded to "Submit yourselves, then, to God" (James 4:7a), before we are told to "Resist the devil" (James 4:7b).