Yes it is rude. Pay attention to the person that you are talking with by looking at them not at other things that might capture your interest. Once you have finished your conversation, you may then focus on something else.
Yes it is.
Because what the person is saying isn't interesting? It is rude in polite conversation, but also human if you see something that captures you're interest which isn't going to last. I think it depends on how well you know the person, if they are a friend and you say look and point it out but then remind them where they left off it might be acceptable.