When a ticket is created, you could send automated emails to agents on your account notifying about the ticket creation. This notification email could be configured under Admin --> Workflows --> Email Notifications -->Agent Notifications-->New Ticket Created.
You could edit the content of the email to add more context. You could also include dynamic Placeholders, which could be used to send more information regarding the ticket like Requester Information and Ticket Properties.
For the New Ticket Created notification, you would be able to add agents to get notified, under the "Notify Agents" section within the same page. You could click on this option and start adding agents who would receive this notification email whenever a ticket is created.
The New ticket created notification email can be set to be sent to agent(s) whenever a ticket is created in your Freshdesk Account under Admin --> Workflows --> Email Notifications --> Agent Notifications -->New Ticket Created.

If the agents do not receive this email, kindly check if it is toggled on. Further, Only the agents whose names are added under the Notify agents section would receive this email each time a ticket is created. You can add as many numbers of agents under this section.

Apart from the default New ticket email notification, there might a Ticket creation automation rule that's sending an email every time a new ticket is created. Please open the ticket from that requester and click on the Activities button to see if there was any automation rule executed on that ticket.
You could navigate to the corresponding automation rule by clicking on the rule link for that activity. From within the automation rule, you could verify if the email notification is being sent, this would be available as an action within the rule. You could remove this action or add another action - "Skip new ticket email notification", to that automation rule, which would prevent email duplication in cases where this rule is triggered.
To turn off this sign up email from being sent to the requesters, please go to Admin --> Workflows --> Email Notifications --> Requestor notifications and turn off User activation email.
This would be turned on by default and all users who raise a ticket would receive this email, after being created as a contact in your Freshdesk Account.
In Freshdesk, you would have email notifications sent out for defined activities on the ticket. You could view the list of these notification emails, under Admin-->Email Notifications.
You could click on "Edit" corresponding to the notification emails listed, to change the content of these emails.
To notify the customer when a ticket is closed or resolved, please navigate to Admin --> Workflows --> Email Notifications -->Requester Notification-->Turn on the notification for Agent closes the ticket and Agent Resolves a ticket. This would send a notification email whenever a ticket raised by them is marked as Resolved/Closed.
There could be instances where you would like to close specific tickets without notifying the requester that the ticket was closed.
In such cases, you could click on the ticket from the tickets list, which would take you to the ticket details page. Within the ticket details page, to the top, you would find the "Close" option. You could click on the "Shift" key and simultaneously click on the Close option.
This would close that particular ticket, without sending out the default notification for when "Agent Closes a Ticket", to the requester.
While setting up SLA, you could configure SLA reminder notifications and SLA violation notifications and choose to send those notifications to specific agents from your Freshdesk Account.
Once this is done, you could setup the first response SLA notification email and resolution SLA notification emails, under Admin --> Workflows --> Email Notifications --> Agent Notification and turn on the First Response SLA reminder, Resolution Time SLA reminder, First Response SLA violation and Resolution Time SLA violation notifications, based on your requirements.
You could notify the requester when a public note is added to a ticket that was raised by them. To enable the notification, please navigate to Admin --> Workflows --> Email Notifications--> Requester notifications --> Turn on the Agent Adds Comment to Ticket notification.
When merging 2 tickets, you can prevent the email notification from being sent to customers that ticket has been closed.
While merging tickets in Freshdesk, there is an option to set as Not visible to contact, choosing which, the merge action will not be notified to the customers. This has to be enabled in all the tickets that are being merged into one, i.e., the original ticket as well as the ticket(s) being merged.
You can also edit the content of the note by clicking on Edit note option as shown below:

Freshdesk has a default email notification which would be sent to customers when they create a ticket. This is editable under Admin --> Workflows --> Email Notifications-->New Ticket Created.
You could edit the Message or Subject of the notification and save it to send a custom notification to the requesters.
We have email notifications for various actions such as the creation of new tickets to add notes. There is a specific one for the assignment of tickets.
Please navigate to Admin --> Workflows --> Email Notifications-> Agent notifications and check if "Ticket is assigned to agent" is toggled on. If it is and you haven't received them - kindly check with other agents if this issue is recreating for them. For further assistance on the same, kindly write to support@freshdesk.com and we would be able to troubleshoot this further.
The automated response the customer receives after a ticket is created is the default email notification or the one you have set up under Admin > Workflows > Email Notifications > Requester Notification>New ticket created. You could view the response and edit it there.