That would hurt PvP more than help it because people would come with 50 splash potions just to throw them from outside PvP. BAD idea
I don't think that they'd work. Just like you can't shoot arrows at people from outside PvP. You both have to be in the arena.
I think it would be a bad idea. If we could fix it so it doesnt affect users outside pvp areas i think there would be some hope for it being accepted.
I think you misunderstood the point of this. This is to enable positive splash potions such as speed and health and not not negative potions such as poison and harming.
They wouldn't be usable anywhere outside of pvp, this is easily done with bukkit. As the same with bows, they won't do anything unless you are inside a pvp arena.
I like the idea but you say just raise the price of string, Well raising the price of string also raises the price of wool, bows, fishing rods becaus they contain string. The prices are balanced currently and that would tip it out of sync.