Work With Filter Web Parts. In the name column it doesnt matter what its called lets just call it FilterParam. With this latest version the default behavior is to only take web parts from the current zone the Content Editor Web Part is placed in and place only those web parts into tabs.
SharePoint List Filter is for filtering the web parts contents according to the specified list of the values. Page Field Filter is designed for working with web parts contents according to the current page information. The latter value has the check next to it.
This managed property should be refinable.
Change the column type to Single Line of Text. The whole query filter functionality seems very flaky at the moment. This managed property should be refinable. We can even provide custom labels for the managed property.