Technically you're not supposed to (have to) do that, if you use the wire nut properly. I never pre-twist them together, and if I ever take a wire nut back off, the wires are always tightly twisted together as they should be. I can't tell you how many wire nuts I've used over the years (done my own wiring, worked for a contractor, etc).
Part of the reason why I prefer the wing nuts vs the round style wire nuts is because you can get some actual leverage without killing your fingers. And they're not as bulky.
Yes.
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No, just no. (Well, the little orange and blue ones are OK for small stuff.)
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