Alert issue

DiVojichi'd check what are the alert settings, if its configured to be sent out immediately or once in week as a summary. Also, would check if the alert mails are getting fired to the exo (but i belive you've tried that too?).

Although Microsoft Article says something very basic but I'm assuming you might have tried all of that already.

can we create another sp list and get the user (with only one account and not multiple) to check if he/she can create an alert and actually getting the alerts to his/her inbox?

also, although you've mentioned that they have full permissions, but its worth checking the permission level for the permission called "Create Alerts" see screenshot. If this box is unchecked then alerts wont work.