Is there a way to send an email notification to the administrator when a specific user logs on to SAP with a dialog logon?
after a user logon, you can call user exit SUSR0001.
Please check Transaction CMOD.
You can enable the audit log by using transaction code SM19 and to view the log by using the transaction code SM20, I am not sure about the email notifications, from the report you can create the Z notfications
Apart from Thorsten's comment, you can consider this SAP Community blog.