In org mode, you can select the entire heading when point is somewhere in the middle with:
C-c p to move to the headline
M-h to mark the "paragraph", which in org marks the entire entry.
Likely not quite what you want, but it seems worth mentioning.
The mouse does seem to work in dired, it's just that it does emacs things, not OS things. :)
For example, on Windows, I can drag a file from the Windows Explorer and drop it into dired and it copies the file -- as OP observed. (Thanks for that, it's nice!)
But for the reverse, if I click on a file in dired and drag, it highlights a region, because click-and-drag in emacs does that. Likewise left-clicking on a file opens the file...in emacs, because that's what hitting RET would do when point is on the same line.
(There is a nice right-click context menu in dired, but it doesn't include anything for
browse-url-of-dired-file
-- bound toW
-- which for the most part opens a file using the default Windows application.)