1) 4mm will be roughly the same equivalent in weight and should hold up fine in non spinner featherweights.
2) Tightly wrap it in tape. A strip of duct tape around the leads held PP3Ds in fine.
3) I'm afraid I don't understand the question
4) Make a mount that the plug either slots into or is clamped by. Being a bit stiff isn't the worst thing in the world. You'll find it will loosen up with use.