Satan offered the world to Christ in one of the temptations.
Scripturally can it be likened to answered prayer by satan when those not in Christ prosper?
Tempting (negative) and answering prayers (positive) are two different things. Satan is not omniscient and cannot read our thoughts, but he can predict our behavior. So, I would say that he can tempt us into doing evil things and thus deceive us into believing that our prayers are answered.
Let's illustrate that with a practical example. A woman prays for a godly husband and is drawn to a soon-to-be-divorced man, handsome and wealthy who tells her that he wants to divorce his wife for unbiblical reasons. Well, if she lives in the Word, she will surely realize that Satan is tempting her.
If you want to deal with the devil, put on the armor of God (
Ephesians 6:11-19).
Are there any Biblical passages to shine light on this?
I can think of one passage where a demon tried to thwart Daniel's prayer from being answered
(Daniel 10).
Daniel fasted and prayed for three weeks and watch what the angel said, "Then he [the angel] said to me, “Do not fear, Daniel, for
from the first day that you set your heart to understand, and to humble yourself before your God,
your words were heard;
and I have come because of your words.
But the prince of the kingdom of Persia withstood me twenty-one days;
and behold, Michael, one of the chief princes, came to help me, for I had been left alone there with the kings of Persia." (Daniel 10:12-13)
Now, Daniel's prayer was heard on day one but answered three weeks later. Why? Because Satan tried to block God's answer to Daniel's prayer.
So that's all he could do based on this example and I can't think of another similar example, but bottom line is that the Bible does not teach that holy angels and let alone fallen ones are omniscient. Nor does the Bible teach that we should whisper our prayers. We are taught to go boldly before the throne of grace.