I do not know what kind of report you are talking about. You can definitely use filters and do quick export to find out how many issues. I suggest you to master JQL and later on also look into creating API using Python which helps a lot.
For example : you can set up your JQL query based on:
project ="ABCD" AND issuetype = SomeIssueType AND status != testing AND ORDER BY DUE ASC. You can also filter based on the dates I think.

Just play with some JQL filters to get customized results. I m sure there might be reporting tools which can do that too. Good Luck.