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I don't know much about aviation, but 1000ft seems kinda close to pass another aircraft. How normal is that distance?

It's fairly standard practice, as long as the aircraft involved are certified for it and flying on autopilot. Given that the planes involved were flying at FL350-60, they probably were (altitudes above a certain threshold - FL290 in the US) are restricted to aircraft operating under rules allowing 1000ft vertical separation.

https://en.wikipedia.org/wiki/Reduced_vertical_separation_mi...

By law, 5 (nautical) miles horizontal separation or 1000 feet vertical separation is required. When aircraft were smaller, that was probably more than sufficient. The A380 is another beast entirely, though.

The question is then - are there any systems that can ensure that two airraft aren't passing eachother at just 1000 feet if one of them is a behemoth? Will the corridors magically widen when an A380 enters it?

Will nearby aircraft be warned when crossing right under an A380 that they are basically on a collision course, while had it been a small aircraft it wouldn't be a problem?

I never understood why corridors at opposing directions aren't by default offseted both in altitude and lateral separation - there have been quite many collision already because navigation aid reduced the positional error within a corridor to few meters

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