Your requirements are a bit vague, so I'm making some assumptions.
For the first one, you want all issues for a specific project (that are not in the Closed state), ordered by assignee - use the following JQL :
project = "xxxx" and status != Closed ORDER BY assignee
For the second one, you want all issues for a specific user, across projects (that are not in the Closed state) - use the following JQL :
assignee="zzzz" and status != Closed
For both, set up the columns to show, run the query and then export to Excel.
I'll give instructions for the cloud based Jira, because that's what I'm using, server may be slightly different.
Click on the Issues menu dropdown and choose Search for issues. If what shows next looks like
then click on the Advanced button. Paste one of the queries into the box and Enter to run the query. There is a Columns dropdown on the right hand side near the top where you can select which columns to show. The middle button in the top right hand corner will allow you to export, either the columns that you've selected or all columns
I hope this helps
@Warren Levy's answer above is perfectly good for JIRA Cloud.
Just wanted to add, that if you wanted any special columns (I'm not sure what 'total' is in your report - but presumably it's number of days from start to end?) - let me know.
I've developed Advanced Export add-on, which exposes just another Export option (as shown below). I can implement export of custom fields or reports if necessary.
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