You can enable/disable email notifications by navigating to Admin-->General Settings-->Email Notifications. However, please note that there are few system notifications which can’t be disabled.

You would need to add agents to the notify agents section available under Admin-->General Settings-->Email Notifications-->New Ticket Created(Agent Notification).

Click on the edit button next to notify agents. Here you can choose the particular agents who need to be notified when a new ticket has been created.
We will be able to enable ticket creation email notifications for requesters. The navigation path for this is Admin -> Account settings -> Email notifications -> Requester notification and enable the 'New ticket created' notification for requesters as shown in the below image.

If an agent is not receiving notifications for new ticket creation, please check with the administrator if the agent’s name has been added to the ‘Notify’ list under Admin-->General Settings-->Email Notifications-->New Ticket Created (Agent Notification)
You can disable the User Activation Email notification under Admin--> General Settings→ Email Notifications to sign up for Freshservice. However, there is no email notification present for the ''User invitation'' email which gets auto-generated from the backend. Read below to understand the difference between User Activation Email and User Invitation Email.
User Activation Email: This email is sent to users when they sign up for Freshservice or any other product under the Freshworks organization for the first time. These users are new to the Freshworks and do not have an existing account with any other Freshworks product.
You can edit this email from the Email Notifications. It can also be enabled or disabled as needed.
User Invitation Email: This email is sent to users who sign up for Freshservice but already have an existing account with another Freshworks product (such as Freshdesk, Freshchat, Freshsales, etc.).
To disable this email, please contact us at support@freshservice.com

Using Freshdesk’s automatic email notifications, you can prioritize your work and be aware of new tickets, customer responses, and much more from within your helpdesk.
Please follow the below steps to edit the email notifications to customize them per your business requirement.
Login to your Freshdesk account as an administrator.
Navigate to Admin from the menu. Select Workflows and click on Email Notifications.
Click on the Edit icon next to any email notification.
You can make use of the “Insert Placeholder” option to add dynamic content and personalize the email subject and its content.
Click Save.

There are default notifications available for requesters under Email Notifications which notify the requester when the status of a ticket is updated to either Resolved or Closed.
We would not be able to stop the close ticket notification for a particular ticket. However, if you use our keyboard shortcuts as below, the closure notification would be skipped for that particular ticket. Try closing the ticket by using the Keyboard shortcut (Alt + ~) or you can press Shift and click on the close button on top of the ticket

We have both First Response SLA notification and Resolution time SLA notification available under Email notifications which can be edited to include custom information if needed. You can navigate to Admin-->Email Notifications and find the notification templates under Agent Notification.

Please note that these notifications work only when you have configured Ticket Escalations setup in your SLA policy
We have a default notification available for requesters under Email Notifications which notifies the requester when an agent adds a public note to the ticket.