How can I get push notifications for emails in my inbox's sub-folders? By default it pushes just inbox emails, not the other folders that are in inbox.
You can't, the Gmail client for Android only syncs the Inbox folder. The other folders are only synced when you enter into each one.
If I'm not mistaken the K9 Mail client have the ability to sync more than one folder.
EDIT to add some new information provided by "Mr. Buster":
The current version of Gmail client for Android phones actualy have this option.
In order to configure the gmail client to sync more than one folder you have to go to:
I have a Samsung Galaxy S2, and i have also got a app called "Email". This was on the phone when i got it, and you can also access gmail trough this app as well as the gmail app.
Maybe this app has the function your looking for.