Is it normal for a nicotine patch to give nightmares or wild and vivid dreams when asleep?

Not Normal, Possible. I would not say it is "normal" but vivid dreams are a possible side effect of prescription doses of nicotine. If these are tolerable, then it may be worthwhile to using the patches to see if things change over time. If they are bothersome or frustrating, then you will want to contact your physician to discuss stopping the patches to see if they go away.