Is it possible to delete a file from a folder via the Dock? I know I can drag the file to the Trashcan but I'm curious if there is some key combination perhaps that I can use to click on a file via the Dock Grid and delete it quickly and without closing that Folder in the Dock.
I'm assuming you're taking about either the grid or fan-out folder on the doc (e.g. documents)? I don't believe you can use the keyboard to select files on the fan-out display (haven't tried it) and thus you'd be limited to the mouse drag method you mention.
For the grid display, you can select files with the arrow keys. However, I would imagine that if it was supported, it would be Command-Backspace (the delete key at the top right of the main keyboard region, not the individual one under the 'insert' key). At least, that would be consistent with the keyboard shortcut for the Finder.