We need to know what you mean by restart. Be specific when you ask a question. But I'll try to answer it anyway.
If you mean making a new world, just open minecraft, go to singleplayer and select "Create a new world". You'll start at the beginning again with no materials or anything.
If you mean re-installing the game if you got some errors or bugs, just uninstall it and download it again. When you have bought the game once, you can download it as many times as you want.
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In order to restart your server, you must close the program you use to host the server, and then just reopen it.
If your Minecraft won't connect to any server simply restart your computer and the router.
If you downloaded the skin's .png you can. Go to the Minecraft home page, log in, and go to your profile. Upload the .png and confirm the skin. Restart your minecraft and it should be working.
The ender dragon resets every server restart.
You just need to restart minecraft its a glitch that sometimes happens.