1. "Pruneface" is used as an insulting description of this man's appearance. To the writer, it seems that the man's face looks like a prune (a wrinkled, dried plum). This is not a real word, but when I read it, I knew immediately what it meant: a face that looks like a prune!
2 and 3. I need to answer these together, because one doesn't make sense without the other! This is rather complex.
To tamper with an image is used literally when referring to a photograph or film -- it means to change that image in some way. But "image" can be used figuratively, to refer to the way someone or something is viewed by people.
So, in this sentence, "image" refers to the reputation of President Kennedy and his officials, rather than to a literal image.
President Kennedy was a very popular president and most people thought the Kennedy presidency was very successful. This question ("Tamper with an image?") is suggesting that Kennedy's success was just "an image" that people would not want to tamper with, because they were happy with it. Phrasing it as a question is a suggestion that people will express doubt about the idea of revising their image of Kennedy.
"A real alternative to what the administration is giving us now" is said in every presidential election when a candidate is running against a president -- maybe not in those exact words, but very close! That is because the current president always has a set of policies in effect, and there are always opponents who don't like those policies. People who don't like those policies want an alternative, a choice: a new president who has different policies.