Delete emails

No. Even if you had a backup you would lose everything else since the backup.

Any more valuable media that gets texted to you, don’t leave it in the delivery system, save it to photos and take weekly backups and/or imports to a computer

If you only recently deleted them then look in the bin or trash or deleted folders.

Mails would not be backed up even if you had backed up the phone.

They are stored on web servers, either iCloud, Google, Yahoo, whatever. Recovery depends on the policy of the account provider.

No