Charlie knew that something about the Cullens was different, but I don't think he had a clue as to what it was that made them different. He did defend them when he thought Bella was judging them like he thought everyone else was, so I think his only real problem with the Cullens was Edward dating his daughter and then all the trouble that followed that Charlie naturally attributes to Bella's "boyfriend". I don't think he ever had anything against the Cullens as a whole, except when they left town so suddenly. Charlie thought that was inconsiderate at the least. Charlie never did find out what they were (vampires) just that they were "special". He only knew enough to let him see his daughter and grand-daughter.
yes, because Edward and Jacob both say in different parts of different books that its easier for Charlie to just believe what he is told and not look too much closer....he doesnt want too much info. but I think he knows the cullens are different, not sure what, but as long as they dont break any laws, he's ok with it.... His reaction to Bellas new appearance after she was changed in Breaking dawn wasnt as shocked as you might think. I know jacob warned him, but I think it wasnt totally a surprise to him. He wondered if Bella knew before she married into the cullens, which Jacob said yes...that seemed to be his main concern
I'm really not so sure....think about how he defended the Cullens throughout the books, especially to Billy. They pulled that into the movie as well. Quite honestly, given my impression of Charlie, I just don't see him spending too much time thinking about it and would take them as they were on the surface - no trouble, Carlisle being an asset to the community, etc. I think any objection he had pre-BD was simply due to knowing how much Edward could, and had, hurt Bella.