When you die, what happens to the money in your pension scheme?
You leave it to the person of your choice.
I imagine it dies with you - the pension provider keeps it
You imagine wrong.
If married, does it automatically go to your widow
No, but it usually would, but you may decide to leave it to the kids.
and then dies when they do?
No it can be left to someone else.
With a S&SISA it is part of your estate, so transfers to next of kin. With a wil in place, you decide where it goes. Is that right?
Yes but assessed for IHT, unlike the pension which is IHT free.
Equitable Life - what went wrong there? Could it happen again?
No. This is COMPLETELY different to how personal pensions work now.
No investment is without risk - what are the risks with pensions?
Exactly the same as any investment. A pension is a set of rules, not something in itself.
I think some financial education is in order.