In the canon Star Wars book, The Princess, the Scoundrel and the Farmboy (by Alexandra Bracken) during Leia's interrogation, we are told that Leia senses some surprise from her interrogator (Vader):
There was...power behind each of his words. They nudged at her. They prodded as sharply as any knife. So Leia did the only thing she could--she pulled back. Physically, toward the wall. Mentally, to a place the voice couldn't find her, a protective blanket that didn't let any of the darkness nudge through. The freezing pressure on her mind was thrown back. The rumbling voice made a sound of surprise and was quiet for a long moment.
Vader stepped back, watching her as still and silently as any poisonous snake about to strike....."Careful," Vader warned. "If you continue to resist, soon you will be neither."
In this scene, it is clear that Leia used the Force to resist the probe to an extent and that her interrogator (Vader) sensed this, resulting in his surprise and silence. Vader might not known of her force sensitivity until this scene. But I am sure he knew after the events of A New Hope.
As for a familial bond, it has been quite clear that Leia had more of a bond with Padme than Anakin (who has more of a bond with Luke). This is made clear with Leia's "memories" of Padme in Return of the Jedi, and several examples in the comics where she sees Padme's protrait turn and stare at her and feeling cold in the Naboo Palace where Maul once stood, implying she feels her late mother's feelings at that time. Due to this, Vader might not of known as strongly of a connection with Leia. This is evident as he never mentions Leia's name even when the revelation is made known to him that he has a daughter:
Return of the Jedi script
VADER:...especially for...sister...so you have a twin sister. Your feelings have now betrayed her too. Obi-Wan was wise to hide her from me...now his failure is complete. If you will not turn to the dark side, then perhaps she will.
VADER: You were right about me. Tell your sister... you were right.
Vader's knowledge seems to be a be limited when it comes to his daughter/Leia, but because we, the audience, know who Luke's sister is, we assume he must know who she is. However, when you really look at it, the two don't have much interaction and when they do, the two don't exactly see eye-to-eye.
But he did sense the force in her during the interrogation but probably thought nothing of it as she was to be terminated during the events of the film; (she also was involved in the Rebellion and hence, a traitor).