To restart something is to shut it down and then turn it back on. You can't restart the server without the part where you turn it off.
Actually there is an inactive plugin called "Restart Me" in another Forum But you need to do a lot of settings You can go sreach it or pm me if you want the website
Actually, all that plugin does is turn off the server, and then the modified start file you have to change to use it just turns the server back on automatically. It's outdated, I'm not sure if it will work.
There may be an updated version of the plugin, but if there is, I have not heard of it. They may also have their own custom plugin.
Custom own Plugin is secret Alot that people custom Enchanted and other things right that don't share it..
Because they worked hard on it themselves, and don't want someone else to use it. It's most common with unique servers though. They're not just going to give someone else the plugins. Not everything is public.
Well, that's kind of off-topic, but I typically use NetBeans for developing/editing my plugins. It works really well, and I really like it.