LAN worlds are available only to people who are on your local network. They have to actually be connected to your network, for the LAN IP to make sense.
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Anyways, yes. LAN worlds are 100% free unless you count internet network costs!
Options > Open to LAN
Yes. It doesn't matter if it's LAN I believe. You just have to download some plugins and put it in the plugins server if you're using vanilla minecraft.
LAN means Local Area Network. LAN World on Minecraft basically means that anyone else playing from the same router/modem as you can join your world.
A LAN world means if someone is playing Minecraft using the same modem/router as you, they can come into your world and play with you.