The "Apply View Filter" menu item can be confusing. We've discussed removing it completely, but haven't gotten around to it. I've used it only occasionally.

(1) I think your suggestion makes sense. We have a similar issue with URL filters when changing views:

https://www.labkey.org/issues/home/Developer/issues/details.view?issueId=11355&_docid=issue%3A11355

(2) That sounds like a bug. We should export the data with the view's filters not applied. I've filed a new bug for this:

https://www.labkey.org/issues/home/Developer/issues/details.view?issueId=17313