It drains stamina, which seems to refill over time like magicka. Every level you choose to boost either max magicka or max stamina. Should be a fun system, especially if there's an athletic perk related to it.
Well stamina (fatigue) has always refilled over time. Also, you choose between health, magicka and stamina when you level up.
Sprinting won't allow you to get away from every fight, you have to realize that the enemies can sprint too.
For more info about sprinting and Skyrim in general, go http://www.gamesas.com/index.php?/topic/1158506-skyrim-information-compilation/ and after reading the info, post your thoughts so that we can keep the thread on the front page. Also, you can leave any questions you have that need clarification there as well.