3. What the best app for reading comics (pdf+cbr)? [preferably free]
In my opinion comiczeal. Its commercial, but the price is 7.99 I think.
Compared to the price of the iPad itself its nothing.
Works perfect for .cbr and .cbz files
I am not so much into PDF, but so far iBooks did not let me down. Not sure about dictionaries though. Also I must admit that the time I read books containing any mathematic formulas is over for me
So I hope other people can answer the other questions you had better than I could