If you want a good test to see if your idea will work. Open a single player world set the the render distance to 4. Quickly mockup the most basic version using /fill and /clone. If it works theres a good chance it will work on the server.

I want to add that I'm actually confused here. I'm not just trying to give people a hard time.

Ok so if B convinces A, A goes to B using TPA, B attacks A, A dies, B get's banned. In all other cases it's ok?

A convinces B, A attacks B, B dies OK
A convinces B, A attacks B, A dies OK
A convinces B, B attacks A, A dies OK
A convinces B, B attacks A, B dies OK
B convinces A, A attacks B, B dies OK
B convinces A, A attacks B, A dies OK
B convinces A, B attacks A, A dies B is Banned
B convinces A, B attacks A, B dies OK

Render distance was 4 last I heard. This page gives a lot of information on spawn mechanics, but doesn't include some bugs that can also have a big effect.
http://minecraft.gamepedia.com/Spawn

@neonjews I can convince a player accept a TPA request and kill them, and because THEY had to click accept, it's alright.

In this first scenario if the person you are trying to kill instead kills you then they should be banned according to what @BaronBattleBread is saying.

@BaronBattleBread Convincing someone to TPA to you, and then killing them is bannable.

Or maybe there's something about intent that I'm not understanding here. It's very confusing the way it's currently explained. Does it all hing on who convinces who? Does it matter who initiates the conflict?

With the random tp someone else can try to tp with you without your permission, but with TPA there's no way for a third party come along for the ride. Only the player that A chooses get's a TPA request and only the player that B chooses get's accepted. So it seams like it shouldn't matter if A attacks B, B attacks A, A kills B, or B kills A.

Here's the options:
A convinces B, A attacks B, neither dies.
A convinces B, A attacks B, both die.
A convinces B, A attacks B, B dies
A convinces B, A attacks B, A dies
A convinces B, B attacks A, neither dies.
A convinces B, B attacks A, both die.
A convinces B, B attacks A, A dies
A convinces B, B attacks A, B dies
B convinces A, A attacks B, neither dies.
B convinces A, A attacks B, both die.
B convinces A, A attacks B, B dies
B convinces A, A attacks B, A dies
B convinces A, B attacks A, neither dies.
B convinces A, B attacks A, both die.
B convinces A, B attacks A, A dies
B convinces A, B attacks A, B dies

I'm both curious which of these are against the rules and why. Also do these rules only hold for a certain amount of time?

Mobs spawns aren't just capped the rate decreases dramatically even if you are half way to the cap.
Also there may be issues with mobs spawning above 126, I'm not really sure.

@RebelGamer101 I'm still working on lighting up all of the caves underneath

Even if you light them all up that won't solve your problem. You really do need to get rid of every spawn-able space to get good rates, and that includes slimes that spawn regardless of the lighting.

@BaronBattleBread Convincing someone to TPA to you, and then killing them is bannable. ...If you accept the agreement for a TPA, and you get killed by the person TPing to you, that is not a bannable offence.

This doesn't make sense to me. If person A teleports to person B. Person A can kill person B but person B can't kill person A.

@RebelGamer101 Thanks for the answer Pand. Good to know I haven't been wasting my time

It's very unlikely that any kind of spawnerless mob grinder is going to work properly unless you have a very good handle on game mechanics. So you very well may be wasting your time.

@BoneChi11er wait then how does the iron farm spawn iron golems? Those things are huge. on a y axis?

I have no idea what you are trying to ask, but here's more information on the topic:
http://minecraft.gamepedia.com/Tutorials/Village_mechanics

Are you trying to make a spawnerless overworld mob grinder?