If you add the Summary Fields extension then you can choose to have a field for 'total amount', total this financial year, count this financial year, etc etc, which then makes exporting much easier as it is 'just' another custom field
When you run the advanced search, change the option at the very top called "Display results as" from contact to contributions. That should allow you to export contribution information for the search results. (There should also be basic contact information available when exporting contribution information.)
Summary fields creates a collection of custom fields that it populates. It populates them when you first set the extension up, and then it also updates them as new contributions are stored.
I suspect that it doesn't recalculate all the fields when you update your fiscal year, you probably need to ask it explicitly to do that, eg. by resaving the ...