"You must first select read access to grant any other API record operation." https://docs.servicenow.com/bundle/tokyo-application-development/page/build/applications/reference/r_TableApplicationAccessFields.html The Application Access configuration fields control the access level for an application and its tables. The following Application Access configuration fields are not available if the Can read configuration field is not selected:
Can create. This field determines whether users can create records on the application tables.
Can update. This field determines whether users can update records on the application tables.
Can delete. This field determines whether users can delete records on the application tables.
These fields are not available because they depend on the Can read field, which determines whether users can view records on the application tables. If users cannot read records, they cannot create, update, or delete them either.
The following Application Access configuration fields are available regardless of the Can read configuration field:
All access to this table via web services. This field determines whether users can access the application tables using web services, such as REST or SOAP.
Allow configuration. This field determines whether users can configure the application tables, such as adding or modifying fields, views, or indexes. Reference: Application Access, Certified Application Developer (CAD) Learning Path

The following is true for GlideUser (g_user) methods:
Can be used in Client Scripts, UI Policies, and UI Actions. This is true because GlideUser (g_user) methods are part of the client-side scripting APIs that provide information about the current user and the user's preferences. Client Scripts, UI Policies, and UI Actions are all types of client-side scripts that run in the web browser and manipulate the user interface.
The following are not true for GlideUser (g_user) methods:
Can be used in Client Scripts and UI Policies only. This is false because GlideUser (g_user) methods can also be used in UI Actions, which are another type of client-side scripts that can be triggered by a user's click on a button, link, or choice.
Can be used in Business Rules only. This is false because GlideUser (g_user) methods cannot be used in Business Rules, which are server-side scripts that run on the ServiceNow platform and manipulate the database. Business Rules use a different API to access the current user information, which is GlideSystem (gs).
Can be used in Business Rules, and Scripts Includes. This is false because GlideUser (g_user) methods cannot be used in Business Rules or Script Includes, which are both server-side scripts. Script Includes are reusable units of code that can be called from any server-side script. Script Includes also use GlideSystem (gs) to access the current user information. Reference: Client-Side Scripting APIs, GlideUser, Business Rules, Script Includes

Application Access is a feature that allows you to control the access level of other application scopes to your application's data tables. You can use Application Access to control the following database operations:
Create: This operation allows the user to create new records on the table. You can enable or disable this operation by selecting or clearing the Can create option.
Delete: This operation allows the user to delete existing records on the table. You can enable or disable this operation by selecting or clearing the Can delete option.
Read: This operation allows the user to view the records on the table. You can enable or disable this operation by selecting or clearing the Can read option.
Write: This operation allows the user to modify the records on the table. You can enable or disable this operation by selecting or clearing the Can write option.
The one database operation that cannot be controlled with Application Access is Query. Query is not an operation, but a method of the GlideRecord class that is used to retrieve records from the database on the server-side. Query is not part of the Application Access rules, but it is affected by the Access Controls and the user's roles.
Reference:
Application Access
[GlideRecord methods]

Business Rule is server-side, so it uses GlideSystem API. gs.hasRoleExactly doesn't exist In a Business Rule, the following returns true if the currently logged in user has the admin role:
gs.hasRole('admin'). This is the correct answer because gs is the GlideSystem object, which provides methods for performing system operations, and hasRole is a method that checks if the current user has the specified role. For example, gs.hasRole('admin') will return true if the current user has the admin role, and false otherwise.
The following do not return true if the currently logged in user has the admin role in a Business Rule:
g_form.hasRoleExactly('admin'). This is not correct because g_form is the GlideForm object, which provides methods for manipulating forms, and hasRoleExactly is a method that checks if the current user has exactly the specified role and no other roles. For example, g_form.hasRoleExactly('admin') will return true if the current user has only the admin role, and false if the current user has the admin role and any other role.
g_form.hasRole('admin'). This is not correct because g_form is the GlideForm object, which provides methods for manipulating forms, and hasRole is a method that checks if the current user has the specified role or any role that contains the specified role. For example, g_form.hasRole('admin') will return true if the current user has the admin role or any role that contains the admin role, such as admin_ui or admin_script.
gs.hasRoleExactly('admin'). This is not correct because gs is the GlideSystem object, which provides methods for performing system operations, and hasRoleExactly is not a valid method of the gs object. There is no method that checks if the current user has exactly the specified role and no other roles in the gs object. Reference: Business Rules, GlideSystem, GlideForm

The fastest way to create and configure a Record Producer is to open the table in the Table records and select the Add to Service Catalog Related Link. This will automatically create a Record Producer with the same fields as the table and add it to the Service Catalog. You can then modify the Record Producer as needed. The other options require more steps and manual configuration. Reference: Create a record producer