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Third, he believes that Mary, along with others who have died, can hear the prayers of everyone who prays for them...that they are basically omniscient, hearing all who pray to them...I don't find this in the Bible, either.

See if Revelation 5:8 proves helpful in this respect:

5:8 Now when he had taken the book, the four living creatures and the twenty-four elders fell down before the Lamb, each one having a harp, and golden bowls full of incense, which are the prayers of the saints.

These 24 elders are already in heaven, and look what they are said to be holding: 1) a harp and 2) golden bowls full of incense, which are the prayers of the saints

Somehow, someway, those 24 dead elders are in possession of the prayers of the saints, which they then put onto the golden altar before the throne (Rev. 8).