Show notifications for all users If I am using a different user on my Android phone, notifications to the main user (owner) don't get shown until I switch back to that user.

This might be for privacy reasons and such, but I see there's already a feature for hiding sensitive notifications (i.e. from the lock screen).

Is it possible to receive some sort of alert/notification/vibration when a new text/email comes in for another user?
I'm sorry there is  no way you can receive the notification of the other user, because according to the concept of 'Users' in android each user represent a different physical user of the device. So the privacy won't let you receive notification from the other users.

Instead of going for another user, you can try 'Managed Profile' which create a separate profile but which belongs to the same user. In the underline architecture you will get almost all the security protection of a separate 'user' to this profile. The main difference will be they are in the same launcher.

Thanks.