How do I access the Player Component and Player Character without the use of local script?

What you could do is make a 'playerAdded event' like so:

game.Players.PlayerAdded:connect(function(player)
	--stuff heer
end)

but say you want to play it on the character, not the player. You'd simply do a character added one right after it.

game.Players.PlayerAdded:connect(function(player)
	--player stuff heer
	player.CharacterAdded:connect(function(character)
		--character stuff here
	end)
end)

-Player: http://wiki.roblox.com/index.php?title=PlayerAdded

-Character: http://wiki.roblox.com/index.php?title=CharacterAdded