This is a self-contained follow-up to a different previous question. Based on the answers I got there I've taken a different approach to my original idea, and now want to try using antigravity on the inside of the balloon instead of the whole ship. Two new questions came up while I was thinking through the concept.
Background: Airships are a staple of fantasy fiction, but in the real world airship design is drastically limited by the amount of lift you can get out of a balloon. I'd like to create a world where compact and elegant airships of steampunk and fantasy are made possible with the addition of just one magical element: an engine that produces a limited kind of anti-gravity. After that, I'd like to keep the physics science-based, with the goal of producing an internally consistent world that still has room for awesome airships.
The Question: I have a handwavium anti-gravity engine. When I put this engine inside a large balloon, and start it, it reduces the effect of gravitational pull (weight) on all the air in the balloon to the point that it becomes functionally as buoyant as a vacuum balloon.
Q1: There is mass inside the balloon, but it now has no weight. Will the air pressure outside still cause the balloon to collapse?
Q2: If the balloon is breached, such as by a bullet, what will happen? There's no lift gas to escape; new air entering the chamber loses weight. So will the balloon keep flying until I rule the magic "reaction chamber" no longer works? Would there be any other effects?
My physics background is confined to Google, so if anything here is muddled let me know in the comments and I'll fix it.