Erpnext user restriction

How a user can be permitted to only one record of the same DocType.

Hello, You can set this in User permission.

Hope this helps.

@simigireesh, Set that record by using User Permissions to respective user.

Refer link -

How can we allow user to only append but not edit a field.

For now you can allow the User to edit the field. Only appending permission is not available out if the box.
Please create a github issue for this explaining the use case.