I think the cover of a book speaks volumes to the person who picks it up. I am drawn to covers which have something to attract me, doesn't have to be a picture. Even the title is sometimes so attractive that I walk away with the book from the store/library. No wonder, Publisher's have a large budget for marketing and graphics for books. Children's books are a heightened example of this. The cover of the book is often how I pick them for my kids to read (but now my children are fast approaching the age when they won't need mom to pick their books - I think I am glad).
Sometimes. If a book has some really nice cover art I'm more likely to be drawn to it. However, as a fan of fantasy and sci fi I've grown pretty used to the idea that great books can have really bad covers. Some fantasy art is incredibly cheesey. I do judge ebooks pretty harshly if they've got Poser art on the cover (done with a program called Poser which creates oddly stiff looking human figures) because if they didn't care enough to pay a real artist I don't expect the story to be very good.
You can often tell the genre by just glancing at the cover since publishers use a sort of visual shorthand to do that. For example, true crime books usually have covers in mostly black, white and red. And then there's the coding for gender they do, where books by female authors are typically given a different look from books by men which can bias the reader before they even open the book. There was an interesting article about gender flipped coversin the Huffington Post recently.
Three things make me pick up a book - the title, the author, or the cover. So yes, I do judge a book by its cover, in terms of that's what catches my eye. I wouldn't, however, assume that I would like or dislike the book based on it.
No, as I'll 'pick-up' a book based on Author's name, especially if I've read one of their book's previously.
Then I'll read synopsis on the back, & decide from that if I'll buy it, or just get it from Library!
I don't buy books like I used to, as now on restricted income! Such is life!