At high enough concentrations. But that's true of anything.

Having a lot of salt or sugar (or any small molecule really) in something makes it impossible for cells to retain enough water to function.

Which is why your sauce/jam doesn't go bad (except at the top, where a layer of condensed water doesn't have the high concentration of sugar or salt).

Ketchup is not raw tomatoes! Home made tomato juice with pulp is usually boiled and canned. It can be stored up to two years.

I don't know, I saw it many times over a fairly long time period. I suppose it could have been a long running prank.

Traditionally you don't add preservative, you ferment the mixture (though without the sugar). This has the advantage of producing more complex flavours but it's more expensive to manufacture because it takes longer. Or you can do it yourself. I make sauerkraut and it is very straightforward.

A big problem with bolognese is that it's not homogenous. So the protection you get from your preservation process isn't the same throughout.

What forbids bolognese brands to add a similar preservative ?