You're supposed to put your dry ice on top - cool air sinks. That's how you keep your stuff frozen. Also, the bigger the block, the longer it lasts - by that I mean don't bust it up...when you bust it up more surface area is exposed to air and thereby dissipates faster.

Dry Ice is solid carbon dioxide - the gas will not harm you, and you can even put the stuff in your drink if you'd like. Just be cautious not to inhale too much of the carbon dioxide gas and you'll be fine.

Do keep a layer between your stuff and the dry ice - a towel usually works fine.