does harnessed dragon get stunned by vex if I play harnessed dragon, choosing vex that's on the BF and killing her?

Yes — Harnessed Dragon still gets stunned. Vex's trigger condition ("when an opponent plays a unit while I'm at a battlefield") is checked the moment the Dragon is played, so the trigger is already on the chain before it resolves; killing Vex afterward doesn't remove a trigger that has already been placed (FAQ #12737). Once the trigger resolves, the Dragon is Stunned and can't be moved by its controller this turn, and it still won't contribute its Might to combat damage (Rule 423.1.b).

Two side notes: you do have to pay Vex's Deflect cost (an additional 1 Power, any domain) to choose her with the Dragon's kill trigger — if you can't pay it, the ability can't be finalized and Vex survives. And the stun doesn't shut off the Dragon — its kill effect already resolved or will resolve normally regardless.