E-Mail notifications only work for first e-mail account (GMail)?
I know push works for iCloud email accounts (@me.com), but as for the other ones, I'm not positive.

You can configure your email notifications by tapping Settings > Notifications > Mail. After you are there, you will notice a list of email accounts. It appears that you have to customize each individual mail account separately. Tap on a email account, and you can configure it to alert you exactly the way you desire to be notified. 

You can also use VIPs (under the list of email accounts mentioned above, or accessed by by tapping the arrow to the right of the VIP mailbox just under All Inboxes in the Mail app) to customize notifications depending on if particular senders are consistently urgent.