Do the Vaal double strike clones attack with the same support gems I'm using? And are they snapshots of my current buffs etc. or are they affected by my buffs in real time?
Do the Vaal double strike clones attack with the same support gems I'm using?
Yes. They are specifically using your Vaal Double Strike skill (but cannot create more doubles with it).
And are they snapshots of my current buffs etc. or are they affected by my buffs in real time?
They are using your skill. That skill updates as your stats change.