NO.. You are only allowed one account and you can use it with as many sites as you'd like.. You should read the Adsense Terms of Service for Beginners ..
u just need to apply once and u put all codes into your other site. becareful not to put into sites that are against TOS
Definatly read the TOS. For each site I would create a different add channel. When you first start out it also helps to create different add chanels for different placements on each of those sites. I did this and it was a great way to see were people were clicking.
If you would like to know how much earnings form each site Adsense channel can help you out and you are not necessary get another adsense account