I'm trying to send invitation to my Facebook friends using FBSDKShareKit
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YES – but only with test users (and not with real users).
These all working fine – but only with test users and not with real users accounts.
The answer to my question I got while writing the question, as I've written it too long, I decided to keep it here and give a answer.
I was not getting push/notifications for real users as I'm trying to invite the users who've already authorised my app. As it require for those real users to remove my app from their Facebook's Settings [Settings > Apps] and then if I'll send him a request they will get it.