Am I required to offer an expiation (kaffarat yamin) if I swore not to speak to my friends, but I didn't complete the word "aklumkum" (to speak to you), and then doubts arose within me that the oath might have been concluded?

This oath was not binding due to its incompleteness, and a binding oath that necessitates expiation is one made concerning a future matter, either to do it or not to do it. It does not appear that expiation is incumbent upon you, as the fundamental principle is the acquittal of one's liability.