Me and my friends were on the Minetown Guest World, and eddminer stole my enchantment table, broke all glass, stole my door, and illegally obtained unlimited lava!

He didn't have the bucket. He cheated to get lava in the block form!

Everything he did was perfectly legal. He was on guest world, where grieifing is allowed, and he either bought lava from the admin shop or used the kit.

More to it: he has spawn eggs!

You can get those by mining spawners...again...legal...

You can collect Lava Blocks by putting a bucket of lava in a dispenser.

Griefing is allowed in the Guest world as it does not reflect our actual main server, it's there to use while waiting for your application to go through.

You can get the eggs by breaking the spawner.

everything listed is allowed in GuestWorld. If he got into chests or doors, you should have /cprivate them to lock them.

I have one question, is eddminer a guest or member?

you can also get eggs from the cash shop

There is no cash shop in the Guest world....