Sword-fighting and teleporting -- how would I do this?

What you would need to do is store each player in two values when they step on the part, and remove them when they get off. And add a while loop to continuously check if both values are valid before teleporting...

local part1 = script.Parent.Part1
local part2 = script.Parent.Part2
local tp1 = script.Parent.Parent.Tp1
local tp2 = script.Parent.Parent.Tp2

local player1 = nil
local player2 = nil

function teleportPlayers(p1, p2)
	-- Teleport them
end

part1.Touched:Connect(function(obj) -- part1 touched
	local character = obj.Parent	-- get the character
	if character:FindFirstChild("Humanoid") then	-- make sure it's a player character
		player1 = game.Players:GetPlayerFromCharacter(character) -- get/set the player
	end
end)

part1.TouchEnded:Connect(function(obj) -- part1 touched ended
	local character = obj.Parent
	if character:FindFirstChild("Humanoid") then
		local player = game.Players:GetPlayerFromCharacter(character)
		if player == player1 then -- make sure the player that stopped touching is player1
			player1 = nil -- set player1 to nil
		end
	end
end)

part2.Touched:Connect(function(obj)
	local character = obj.Parent
	if character:FindFirstChild("Humanoid") then
		player2 = game.Players:GetPlayerFromCharacter(character)
	end
end)

part2.TouchEnded:Connect(function(obj)
	local character = obj.Parent
	if character:FindFirstChild("Humanoid") then
		local player = game.Players:GetPlayerFromCharacter(character)
		if player == player2 then
			player2 = nil
		end
	end
end)

while true do
	wait()
	if player1 and player2 then -- check to see if player1 AND player2 are valid players
		teleportPlayers(player1, player2) -- teleport them
		player1 = nil -- reset values
		player2 = nil
	end
end

In terms of one of them dying, what you could do would be inside of the teleportPlayers function is make a Player.Character.Humanoid.Died:Connect(function() ... end) to check if either of them died.

https://wiki.roblox.com/index.php?title=API:Class/Humanoid/Died