Intermittent electrical problems are hard to pin down. In a situation like yours, I would start by checking the battery. A bad battery can cause all kinds of issues. Once you are sure the battery is good, I’d recommend checking all the body grounds to make sure they are secure and free of corrosion. If the problems still persist after doing that, then I’d start taking a closer look at the modules and wiring involved with the circuits you’re having issues with.
More info on solving problems like this here: http://www.ericthecarguy.com/faq/solving-automotive-electrical-problems
Good hunting and please keep us updated.