They are what attaches the cooler to the motherboard and mounts it on top of the CPU. The only thing wrong with them is they are so darn annoying to install because they slip easily and just aren't as straight forward as "Screw this here to hold this in place." The push pins are more like "Push down on opposite corners then twist 45 degrees to lock, all while performing a barrel roll of an 80 story sky scraper and scrambling eggs on the way down."
To answer your question, no you can't just go out and buy screws for them. Only certain heatsinks have this type of mounting method, and if the heatsink doesn't initially come with this option, it's probably very hard to find one for it.