hi There,

Is there any idea how will I get to know when or by whom one particular "mailbox or the mail contact" has been deleted from the exchange server? 

Do we need to enable the audit to ensure the events are captured? if yes what type of audit has to be enabled? how it is to be done? what are the pre-requsites and dis-advantages? 

Hello

tip:  open to ecp--> compliance management --> auditing and open "view the administrator audit log../

You can use administrator audit logging in Microsoft Exchange Server 2013 to log when a user or administrator makes a change in your organization.

To enable auditing, you may follow this resource : https://technet.microsoft.com/en-us/library/dd335144%28v=exchg.150%29.aspx

To view the administrator audit log, please walk at: https://technet.microsoft.com/en-us/library/dn342832%28v=exchg.150%29.aspx

Moreover, If you wish to audit such changes automatically, you may also consider on LepideAuditor suite that lets to track every critical actions into real time and alerts instantly by sending customized email notification.