All retractable aircraft (single and twin) should have the horn/buzzer. Being able to cancel it in certain configuarations should be a given (ie - low power, clean flap, gear retracted, on descent) but once there is flap out beyond the first stage (ie landing flap but gear still up) the horn shouldn't be able to be cancelled.
I don't think the twinstar has the 2-stage cancel ability - it just blares ALL the time - as soon as one power lever is retracted.
And you can't do a 'zero thrust' position, as it's only a single lever control on the fadec engine.