IPhone – Gmail doesn’t work with default Mail app on iPhone 6 with data only

Don't use that guide. In fact, don't use the gmail option either, if you can help it.

Use google's own advice which suggests setting it up as a Microsoft Exchange server. that will get you syncing with mail, contacts and calendars. But the main benefit is that it gives you true push syncing!

It's probably a little redundant, but here is a shortened version of the list of instructions.

1. Select Microsoft Exchange account
2. In the Email field, enter your full Google Account email address. If you use an @googlemail.com address, you may see an "Unable to verify certificate" warning when you proceed to the next step.
3. Leave the Domain field blank.
4. Enter your full Google Account email address as the Username.
5. Enter your Google Account password as the Password. (If you are a 2-step verification user, please use an application-specific password instead.)
6. Tap Next at the top of your screen.
7. Choose Cancel if the Unable to Verify Certificate dialog appears.
8. When the new Server field appears, enter m.google.com.

You can then choose which items to sync, choose whether to keep existing contacts on the iPad etc.

Keyboard shortcuts: Mail has it's own keyboard shortcuts, which you may have to learn.

Alternate email addresses/multiple accounts: works fine. Don't know about plus-addresses.

Priority inbox: this is not supported. Labels work, as does flagging. Public calendars work in iCal.

Syncing is very easy to set up - via IMAP in Mail, and in Preferences in iCal. In Lion it's even simpler.

Yes, you add each account separately in mail. You can still visit them in any browser or device.