Bukkit is an Minecraft Server Hosting software.
Bukkit is an API (application program interface) that changes the way plugins interact with the minecraft program. Most server mods will use Bukkit instead of attempting to 'hook on' to the actual minecraft software.
You can't
Yes, this mod is available for singleplayer
Minecraft commands were first seen in bukkit server. We do not know when the first commands were made for bukkit servers however
There are Bukkit plugins already available to do that on Bukkit Minecraft servers, but they haven't released any information on actually implementing that into the game.
bukkit
wrong bukkit version.
No
you cannot set up permissions in a normal minecraft server. you must have a bukkit server to use permissions. check the bukkit forum for more info.
You can download minecraft plugins from planet minecraft minecraft forums bukkit (for multiplayer) mods for minecraft.com mods for minecraft.net
On a bukkit server, if you have permissions, you can do /thunder, /lightning, /smite or commands like /weather set storm to get the thunder/lightning effect. It all depends on the commands you have on a server. In singleplayer you would have to change the weather by doing "/weather thunder"