استلم إخطاراً

Yes, but only if the email is an official notification (like from a service provider). For a personal email, use 'risālah'.

Not necessarily, but it is always 'serious' or 'official'. A notice of a tax refund is still an 'ikhṭār'.

'Ikhṭār' is more formal and legal. 'Tanbīh' is a general alert or a 'heads up'.

You say: 'لم أستلم الإخطار على هاتفي' (Lam astalim al-ikhṭār 'alā hātifī).

In formal writing and speech (Fusha), yes. In casual speech, people often say 'ikhṭār' without the 'an'.

Yes, you can 'tastalim hadiyyah', but you would never call a gift an 'ikhṭār'.

It is a 'Return Receipt' or 'Acknowledgment of Receipt' for mail.

The roots are present, but this specific administrative collocation is a product of modern legal Arabic.

No, 'ikhṭār' is a noun. The verb is 'akhṭara' (to notify).

It is considered B2 because it involves administrative and formal vocabulary used in specific professional contexts.