I play a unit when vex on battlefield and i kill vex does the stun and unmovvsble still applied?

No — the Stun and the "can't move it this turn" restriction both stay put. Vex's ability isn't a "while Vex is on the board" effect; once the trigger resolves, it applies a Stunned status and a movement restriction to your unit with a fixed duration ("this turn"). Vex leaving play afterward has no effect on either (FAQ #12412).

Both expire together during step 3d of the end-of-turn cleanup, so your unit stays stunned and immovable by you for the rest of the turn (Rule 423.1.a.2, Rule 317.2.c).

One edge case worth separating: if you kill Vex in reaction, before the trigger resolves, then the ability fizzles and nothing gets applied — but if the stun already landed, killing Vex changes nothing.