What is the biblical evidence for God's omnipotence and omniscience? Does God tell us in the bible he is omnipotent and omniscient, or are these attributes which (Greek?) philosophers and theologians merely ascribed to him?
A simple Bible search for 'almighty' would have given you more than enough passages about omnipotence. The first mention, for example, is:


  Genesis 17:1-2 (ESV)
   1 When Abram was ninety-nine years old the LORD appeared to Abram and said to him, "I am God Almighty; walk before me, and be blameless, 2 that I may make my covenant between me and you, and may multiply you greatly."   


For omniscience, similarly many, many passages exist -- the combination of them shows quite strongly that God is omniscient. For example:


  1 Samuel 2:3 (ESV)
   3 Talk no more so very proudly,
  &nbsp;&nbsp;&nbsp;let not arrogance come from your mouth;
  for the LORD is a God of knowledge,
  &nbsp;&nbsp;&nbsp;and by him actions are weighed.  
  
  1 Samuel 16:7 (ESV)
   7 But the LORD said to Samuel, "Do not look on his appearance or on the height of his stature, because I have rejected him. For the LORD sees not as man sees: man looks on the outward appearance, but the LORD looks on the heart."   
  
  Matthew 6:4 (ESV)
   4 so that your giving may be in secret. And your Father who sees in secret will reward you.   
  
  Acts 2:23 (ESV)
   23 this Jesus, delivered up according to the definite plan and foreknowledge of God, you crucified and killed by the hands of lawless men.