There's definitely high frequency algos that deal with options.
Thats a pretty weak argument to say volume contributes to volatility, and algos contribute to volume, so algos are the reason why markets are volatile. You have no justification of why algo trading has a different market impact than regular trading. Also, does the VIX depend on volume? Because earlier this year, the VIX index would be pretty high even though there was little trading volume.
Also, S&P Cash index is calculated every minute, while S&P futures changes every moment. So naturally, if there is more volume on the S&P, there will be more differences with the Cash Index because they are calculated at different intervals and there is more trading intraminute. If S&P Cash Index was calculated every moment too, there would be much less differnces.