an aftermarket cooler could be transferred to a new build. Overclocking may help, but its not going to be easy on that processor, as it will have to be FSB overclocking.
Could be, but spending 50 for a heatsink, and overclocking an old processor with an old motherboard that is very limited, I think his money would be better spent, Ideally on a new motherboard, processor (either AM3 or go towards an i7), ram, and cooler. That would take care of his lag.
But, the cheep est way, would be to just pick up some Arctic Silver and a good universal heatsink. Xigmatek makes a really good budget cooler thats very universal. But even with that, I am afraid you would still need a better motherboard for optimal overclocking.