Grievous doesn't attempt to block blaster bolts in the movie, true, but then you could argue the only time he was being directly fired upon he didn't have his sabers...
Given his speed and such, in CW, I don't see why he couldn't have just spun his sabers like a "shield" to block the bolts. They give us the impression that he's just mechanically obeying Dooku's admonition to "retreat" rather than attack. I think they threw that in there because had built up Grievous to be this fearless unstoppable combat monster who kills Jedi Masters with ease. Then they find out RoTS is going to have him as a coughing coward who doesn't directly kill anybody (except maybe a few Clone Troopers he runs over in that jallopy of his) so they introduce this to try to explain the change.
Where in the movies and books did it say that Dooku was Qui-Gons master?
In AOTC when Obi-Wan is being held prisoner, Dooku says (iirc) "You forget, I was once his master as he was your's," something along those lines anyway. But yeah, Yoda taught Dooku. Dooku taught Qui Gon Jinn. Qui Gon taught Obi-Wan Kenobi. Obi-Wan taught Anakin, then Luke. According to the movies...