If you somehow manage to cast this while other spells are on the stack, those spells won't be countered.

This has the supertype world. When a world permanent enters, any world permanents that were already on the battlefield are put into their owners' graveyards. This is a state-based action called the "world rule." The new world permanent stays on the battlefield. If two world permanents enter at the same time, they're both put into their owners' graveyards.

You choose which opponent makes the choice. Null Chamber does not target that opponent.