Can I save part of a previously saved word?

Because clicking on a highlighted word opens up the LingQ Widget to that word, you can't select a part of a word you have already saved unless you turn off the highlighting. You can turn the highlighting on and off at the bottom of the Saved LingQs tab on the right.

Any partial words you select will not appear in the Saved LingQs list for the item you are in. They will, however, still be in your full list of Saved LingQ's in Vocabulary. You can also add any word you like directly in the Vocabulary section.