Why are SPX options more volatile than SPY options?

I have three main questions:

1) You can’t directly invest in SPX. It’s just an index of the S&P 500. But you can buy an ETF like SPY that tracks it. Is that correct?

2) Even though you can’t buy SPX directly, it does offer many highly liquid options. Why does SPX have so many options, yet doesn’t offer the ability to buy SPX directly?

3) And finally, why are SPX options more volatile than SPY options? They seem to offer much more upside and downside.