The downloads.sqlite is no longer used in current Firefox releases.

Download history is stored as part of the normal browsing history (visited sites/links) in places.sqlite and a special annotation property identifies such an history item as a download item, so you can't separate them easily.

• Downloads are treated as history items: clearing history removes included download items and vice verse.
• When downloads are in progress you see an animated download button on the Navigation Toolbar showing an estimate of the remaining time
• The Download button gets a green highlight once all download are finished to make you aware that new downloads are available.
• Pause and Resume can be found in the right-click context menu of an item.

You can display the new Downloads Manager in a tab by opening the about:downloads page and You can consider to open this page in a separate window.

Are downloads now included in syncing, like bookmarks are?