I can't give a definitive answer to the red tag (they're not dangerous, though), but files are marked as red before they're hashed. Just add a folder to share with a few files, and you can watch them change color in the library pane as they are hashed (all the other library stats will be reset too).

The download.dat/bak files keep track of which pieces of the file have been completed, at least, and probably more. I think of it as an index LW uses to checklist what a file needs before it's considered 'complete'. btw--the T-### in front of an incomplete file name is the predicted number of bytes of the final file size.

For exploring the incomplete folder, just set it to list view. They are being rewritten and moved often, so the icons will be constantly moved and deleted. Otherwise, if you want to keep the icon view, set the OSX finder's folder view options to sort automatically.

There--now the experts can give a better answer. Happy Easter