I don't think there's a way to export the built in home/mywork pages. You should be able to create a report that mimics it. Keep in mind there are a number of options you'd have to factor in.
Do you want tasks and issues, or just tasks? If it's the first, you'd need to build a 'work item' report rather than a task report Note that while the work item report includes tasks and issues, they tend to have different columns. So for one look, you tend to build a lot of valueexpression fields using IF statements to show either. For the completion date of the item, for example: valueexpression=IF(ISBLANK({taskID}),{opTask}.{plannedCompletionDate},{task}.{plannedCompletionDate})
Do you only want things that are ready for them to start, or things that still have incomplete predecessors? If you only want the items they could pick up and do now, you'd want to filter to see if it had handoffDate or if canStart is true
In layout templates you can select which fields (including custom fields) display when you select something from your home page, so there's no universal answer for what other columns to include in your report
Users can choose to group by the week it's due or the project (or priority or commit date) so you would want to ensure they have access to these as groupings in their layout interface, and allow them to change groupings on the report.
Barry Buchanan - WMA Work Management Australia