No. Diet drinks have been implicated in contributing to gulf war syndrome, desert storm syndrome, and may provoke migraine headaches in susceptible people. There is no evidence that any food additive causes multiple sclerosis, but some anecdotal comments raise concern of a potential to trigger a relapse, but no proof yet.
Good question. . There are some doctors that are concerned that aspartame (the sweetener in diet coke) could be toxic in certain situations. Aspartame breaks down into formaldehyde at temperatures above 87° & the toxic effects of formaldehyde could lead to neurologic disorders. However, there are no rigorous studies to support this thesis. Aspartame may precipitate seizures in little children, so they should not.