#2
no

If used properly.
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#3
Same as other guitars. If you keep it/store it on the headstock you will eventually damage that. Gotta think leaving it on the guitar in position could work that slow damage to your nut that storing a pick near there between the strings would do. However I'd spend the money to get a quick clip on/off with tension adjustment capo with padding for the neck made of aluminum instead of those wrap-around and tighten or snap a clip to seat ones. You'll thank yourself later.
#4
I used to hate capos on electric but eventually figured out that you can put it on the fret itself. It sounds great and won't bend the strings.