Hello,
1. You can use Jira out of the box tools to import issues. You can read more here:
But you would need to grant Jira Administrator global permission to the user.
2. You can develop your custom solution, using Jira Java API or Jira Rest Api. In this case you would need to give the user or the proxy user permissions to login to Jira and create issues.
3. You can use Issue Collectors. You can read more about Issue collectors here
https://confluence.atlassian.com/adminjiracloud/using-the-issue-collector-776636529.html
In this case users do not have to have an account in Jira
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