I have an iPad Air and all I want is -when the iPad is asleep and not charging- to get email notifications as soon as they are sent and FaceTime alerts as soon as the call is made.
At the moment when the iPad is asleep and not charging I do not get email alerts but can receive FaceTime alerts.
Unless your email provider has Push Notifications (and you said they do not), you can not get mail notification on your iPad as soon as they are sent. The best you can do is set Fetch to 15 minutes. This will have some impact on battery life, compared to the 30 minute option, but not a lot.
The iPad should perform the Fetch whether it is plugged in or not, asleep or not.
For a proper test, don't just wait for emails to come in. Use your computer to send test emails, so that you know when they are sent. Hold in mind that the response time will vary, since the iPad is checking on a schedule; every 15, 30, or hourly. At a maximum it should not be much over the time set; holding in mind that the email servers can sometimes have delays in delivering email.
Facetime does have Push Notifications, which is why it works immediately. Being a live call service it would be pretty useless otherwise.
If it is absolutely necessary that you get emails as soon as possible, you should consider changing your primary email provider to one that supports Push Notifications. As an interim measure (while you migrate your contacts to the new service) you can probably have BT automatically forward to your new provider. Noticing which emails are forwarded will also tell you where you need to go to make changes.
iCloud, Google, Yahoo, and Hot Mail all have Push Notifications. I'm not sure about others, especially the U.K. providers.