It sounds like electrical wiring problem and those are hard to diagnose over the internet but I probably can help you with one problem which in turn may dry out and help your other problems.
If you run your finger along the bottom jamb, or if you are good looking up at the bottom jamb with a mirror you will find, usually oblong but shape doesn't matter. There are hole, maybe two maybe three per door. Poke in those holes with a nail or something to clear the debris that is blocking it from draining. You can take the panel off and really clean it but I like the lazy man's way of remembering to unplug the holes after every rain.
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