Your answer is yes, all of the above. Each variable has to be taken into consideration when they are selected to manufacture and reflow BGA components.
The types of flux in the solder paste needs to be evaluated for its ability and capability to absorb moisture and this will define part of the thermal profile ramp up, as any absorption has to be dried out for good reflow. Secondly excess solder paste and the solderability of the paste is important as we need the solder paste to coalesce into one solder ball at the joint of the BGA component. If the solder paste is not solderable it will short to the adjacent pads.
The profile is important as it impacts how the board and the BGA component will warp and twist during the reflow cycle. Plastic BGA components will warp and twist and when they push down on the board they compress the solder paste and shorts are created. This is typically seen at the corners of the devices. If you have popcorning, or moisture in the component, the belly of the component will blow out and when this occurs the middle of the component will push against the solder paste and you could end up with shorts in the center of the component.
Design of Experiments should be conducted on the products to determine the best operating parameters for the reflow profile on BGA components.