Trying to understand Mountain Lion's Notification center

Hi guys,

Since i installed ML, everything is going great, even notification center is amazing. But just few things I am not clear on

1. Mail notifications - Does mail app or lets say sparrow app really need to be open to receive notifications? I read online that notification center doesnt mean you are going to get push alerts automatically, but already existing apps will use local alerts like it was before ML, but instead just push it to NC. So this means I cant close Mail app? Even for iCloud mail which does push?

2. Reminders, calendar alerts work fine without the app needing to be open. Was that the case before as well? I cant recollect

3. Any way to customize the alert sounds? Or will apps use the standard OS X alert sound?