Why did he send his approval to William before the invasion, what was his hate towards Harold. Sources would be much appreciated
He didnt hate Harold, was probably barely aware of him. Simplistically put however there had been an ongoing dispute over who was Pope, Alexander II or Honorius II. The former elected by the Church, the latter elected by the German court of Henry IV, via his mother as he was still a kid. The Sicilian Normans, once in disagreement with the Papacy, were now aligned and supportive of Alexander II. Its therefore no surprise that when the Norman Normans turned up wanting a favour that the Pope would agree. Firstly because it kept the Sicilian Normans onside and secondly because it 'proved' that he was the Pope with Authority, unlike that other Pope. Additionally when you only hear one side of the story you may be more inclined to believe it.
Theres no primary source I've come across that will say 'and so Pope Alexander II, who hated the Anglesaxon King...', as its more inferred by surrounding issues and events. However this is a start. http://books.google.com.au/books?id=Sf8-AQAAMAAJ&pg=PA206&lpg=PA206&dq=%22pope+alexander+Il%22&source=bl&ots=J1UzfTM8Nh&sig=2uaprlwj5mm2p7ReiPbtkCBoMIw&hl=en&sa=X&ei=nuokVJamNIvjoATEmIHABw&ved=0CDkQ6AEwBA#v=onepage&q=%22pope%20alexander%20Il%22&f=false