Very well explained merlin3189. From above what I can gather is:
1. If balls are in vacuum, buoyant force will be same on both A and B (since weights are same)
2. If another lighter fluid is above water, then buoyant force due to the other fluid will be more on A as compared to B because more of...
For the 'floating' question, if we take the atmospheric pressure into account, then force due to atmospheric pressure (downward) will be more on the bigger ball (greater surface area). The job of the buoyant force is to balance the weight and atmospheric force. Weights of A and B being equal, as...