Do processors include heatsinks?

The vast majority of retail boxed CPUs come with a HSF unit with thermal paste pre-applied. All you need to do is insert the CPU and install the HSF unit. You can find plenty of tutorials on doing this on Youtube. Good luck!
 
Retail boxed always do. It won't be fancy but it will do the job assuming no overclock. If you intend to overclock you'll want to shop around for a better fan.

If the chip you bought was marked "OEM", Original Equipment Manufacturer, it won't have one. Again, with no overclock the minimum fan you can find to fit your socket will work.