If I use Facebraker in a battlefield where I have a unit, can I play it without an enemy in there?

No. Facebreaker requires both a friendly unit and an enemy unit at the same battlefield as valid targets when you play it — you can't play it with only your own unit present (RiftJudge FAQ #40).

The "stun a friendly unit and an enemy unit" wording is a group targeting requirement, so the play is illegal and cancelled if either target is missing. Having just a friendly unit isn't enough.