Mail App related Queries

I have created certain labels for my Gmail and want to see the notifications of those mails only which are part of the Primary tab of my Inbox. But the problem is, whenever I turn on the notifications for the Mail App, notifications of all the mails landing in my mailbox are getting popped up which is kind of unnecessary.

Plus, I have some Labels created for my Gmail to ease the mail reading/prioritizing process. Those Labels also dosnt show up on the home screen of my Mail App. I am thus forced to use the Gmail app.

Is there any way I can get the notifications for only those mails which are part of the primary tab of my mailbox and also, can I make the Labels visible too?