If you want to select text and copy it to the clipboard using only the keyboard, you will need to show caret. Then you can use arrows to move the caret, hold Shift to select text, and Ctrl+C to copy the selection to the clipboard. To switch between the left and right file views use the Tab key.
To show/hide the caret:
|File Comparator menu:||View/Show Caret|
|File Comparator shortcut key:||F2|