Minecraft Portal/Teleporting between 2 Overworlds

Just make sure there's at least a 1025 blocks distance between your overworld portals:

Likelihood of 2 overworld portals linking to the same nether portal - Normal World portals that are within 1024 distance of each other on either X or Z axis are almost always going to link to the same Nether realm portal on initial construction because 1024 translates to a distance of 128 in the Nether Realm, and the game checks for existing Portals within 128 "radius" around the destination (the 257x257x128 box).

(Minecraft Wiki)

You should also note that, in SMP prior to 1.6, portals were bugged for quite some time and needed server mods like Bukkit in order to work. Ask your admins/operators, there may still be some Bukkit plugin running on your server handling the Nether.

For servers like Mineplex, they most likely use a plugin, simply because they're more configurable and reliable.

If you want to shut down the server at a specified time, that can be easily done with various pre-existing plugins. From a Google search I found AutoShutdown. This basically shuts down and restarts the server at times you can specify, along with some other features. Just before the server shuts down you can kick all the players to a lobby using, maybe, BungeeTeleporter.

However, if you want to shut the server down when a game ends, that may be more complicated. Doing so would probably require that a specific condition be filled for the game to be counted as over, such as only 1 player left alive, or a timer runs out. I haven't found a plugin for this, but if you're proficient with Java and plugin development it's possible to make your own.

You may also want to reset the world when the game is over to prepare for a new match. I recommend WorldReset to automatically restore from a backup.