But a big fire will do a lot of damage and expose that iron to the weather--it will rust away. By the time civilization is recovering all that will be left is what's underground.
Food for 10,000 people for a day is equal to food for 10,000 days for a person. The non-perishables in just one surviving grocery store would feed a handful of people for months, maybe years. And anyway, most survivors are people who already know how to live off-grid in harsh environments - see above
No, because most of it won't last anything like 10,000 days.
Besides, you're looking at what would happen if the people were killed off first--in that case the survivors could do quite well by salvage. That would only be a likely scenario if the threat was biological. In that case I think we could rebuild.
However, in the war or impact scenarios you have more mouths than supplies--if that grocery store survives it's going to be stripped bare in hours.
And 10,000 survivors in one community is viable. 10,000 survivors in 1,000 scattered groups probably won't make it.
We probably have already catalogued all dinosaur killers in ordinary orbits and it doesn't look like there are any serious threats. New comets show up all the time, though--and our chances of a successful deflection mission against one is a big, fat goose egg. The risk is low, not zero. Remember 4 years ago where the Martians got a serious case of pucker factor?
Yes; I said 'on the cusp of' - we are not quite there, but we can see how to get there from here.
We are on the cusp of being able to deflect a rock with a lot of warning. If they find a dinosaur killer 10 years out I would think they would get it. You don't need much deflection that far out, if the rock is solid enough a single h-bomb will do it, if it's a gravel pile it will take several smaller bombs spaced out over time. (Against objects that lack strength you're limited to deflections well below it's escape velocity so it doesn't come apart when it's hit.)
Now, if it's something like the one that scared the Martians it's quite another matter--trying to deflect it would actually be a bad idea, the effort should be spent digging in instead.
Maybe there would only be 10 million. or 1 million, or even as few as 10,000 people left. Those are STILL viable populations:
10,000 is certainly non-viable--that's going to be a bunch of scattered individuals who don't know where others can be found.
A burnt out city is not a harder to reach resource than the ores that were used in the early Bronze and Iron Ages.
A burned out city will leave behind stuff that
rusts. There won't be much metal left within a few generations.
The ENTIRE annual iron production of the Roman Empire at its peak was less iron than is found in one large modern container ship. You don't even need to go to a city - there will be VAST resources (by Iron Age standards) washed up on beaches all over the world.
Rust.