One tomato in the pack went mouldy — is the rest of the pack fine, and is the answer different for hard vegetables and cheese?

The reasoning you are after is about structure, and once you have it the contradictory rules stop contradicting.

What you see as fuzz is the fruiting part. Underneath it the mould has a root network — hyphae — growing through the food, and it goes much further than the visible patch. How much further depends entirely on how dense the food is.

• Soft and high moisture — tomatoes, berries, peaches, bread, soft cheese, cooked leftovers. The hyphae spread easily and fast, so by the time you see the patch the network is well beyond it. There is no safe margin to cut, because you cannot see where it ends.
• Hard and dense — firm cheese, carrots, cabbage, hard salami. The structure physically resists the spread, so the network stays close to the visible growth. This is where the "cut around it" rule comes from, and the usual figure is about 2-3cm on all sides, with a clean knife that does not touch the mouldy part and then the good part.

Your cherry tomatoes are firmly in the first group as individual fruits. But that is about the mouldy one, not its neighbours.

On question 1 specifically, and this is the part that reassures people: mould spores are everywhere already. They are in the air in your kitchen right now, on the skin of everything you have bought, and always have been.

So the mouldy tomato is not the source that contaminated the others. It is the one that had an opening — a split skin, damage at the stem scar, a bruise — where the spores that were already present found their way in. Intact skin is a genuinely good barrier, which is why one fruit rots while the one touching it does not.

What that means practically: inspect the rest rather than binning them. Check each one for soft spots, splits and anything weeping at the stem. The sound ones with intact skin are in the same condition they were in at the shop. Use them soon rather than in five days, because proximity to a heavy mould source does raise how many spores are sitting on the outside, waiting for the first bruise.

Washing: it does something, and it is not what people hope.

Rinsing removes spores sitting on the surface, which is worth doing and will slow down how quickly the rest of the pack goes over. It does nothing whatsoever about a network already growing inside a fruit, because you cannot rinse the inside of a tomato.

One genuine trap: wash them when you are about to use them, not when you get home. Washing leaves moisture in the stem scar and in any tiny crack, and that moisture is the thing mould was waiting for. A washed and re-boxed punnet goes over noticeably faster than an unwashed one.

The storage version of this: get them out of the sealed plastic. Those packs trap the moisture the fruit gives off, which is why the bottom layer is always the one that goes first.