Does anyone have any personal experience...
Yes, I've fasted (water only) for 30 days. My fast is described in this entry on the Perfect Health Diet blog.
...or scientific/medical information to support/refute any of these notions?
There are many peer-reviewed papers on fasting going back to the nineteenth century... hundreds of them. Nobody can summarize this literature here; there's too much information. Here's a good general review article on fasting from the medical literature:
Here's a fascinating article about the longest fast in the medical literature. This guy fasted for 382 days.
You ask about absorption of unwanted tissue. This is called autophagy. Fasting induces high levels of ketosis, and ketosis promotes autophagy, so yes, most likely fasting does promote resorption of some unhealthy material in the body. Whether that material includes atheromas, I don't know. I don't recall seeing any papers on that subject but there may be some.
Edit: It just occurred to me that if any such paper exists, it would be cited in Joel Fuhrman's book Fasting and Eating for Health (see citation below). Sure enough, on page 113 he claims that there is one paper that showed regression of atheromas in fasted nonhuman primates.
However I just read the paper and it shows no such thing. The nonhuman primates weren't fasted; they were put on either a low-fat diet or a diet supplemented with a particular kind of fat. Fuhrman misrepresents the study. Here's the paper if anybody wants to check:
Evidence of regression of atherosclerosis in primates and man
There is evidence that fasting (or deep ketosis induced by extreme ketogenic diets) can kill some types of cancer cells. (Fasting and extreme ketogenic diets are related because ketogenic diets simulate fasting.) Just a couple of months ago, the first paper was published describing a successful use of this therapy in a human patient. This patient's brain tumor shrank. However it probably didn't shrink because of autophagy. It probably shrank because the cancer cells starved to death, due to the fact that cancer cells cannot use ketones for nourishment. The paper is here:
One of the scientists who is involved in this anti-cancer work is named Thomas Seyfried. He advocates fasting for seven to ten days once a year as a preventative measure for cancer. If you google his name, you'll find a couple of interesting interviews with him. For example:
Jimmy Moore interviews Thomas Seyfried
I'm describing peer-reviewed science here. There are also popular books written by doctors who have lots of clinical experience supervising therapeutic fasts. They make many interesting claims about cures of various diseases. Whether these claims are true, I don't know. The best recent book of this type is this one:
Furhman, Joel. Fasting and Eating for Health (1995). St. Martin's Griffin: New York.
Finally, let me give you a link to a fascinating interview with a woman whose unremitting 16 year headache (due to inflammation of the dura mater) was cured by fasting. She's a patient, not a doctor or scientist, but she's extremely intelligent and articulate.
16 year chronic headache cured by 41 day fast