Is hydroponics and aquaponics considered agriculture?
Of course. The definition of "agriculture" contains no mention of soil.
Yes Agricultue includes the growing of food (plant and animal) by whatever means. Much agriculture takes place in water - rice for instance. The practice of growing without any soil is an extension of the traditional growing methods. It may become more important if self-sufficient human colonies are established on the moon or Mars.
Yes, hydroponics, aquaponics, and other growing methods are a form of agriculture. To be more specific, they are considered a branch of CEA: Controlled Environment Agriculture.
Yes and you can be assured every hydroponic grower that grows in a greenhouse knows elevated levels of CO₂ in the air as beneficial to point where they'll have CO₂ generators in the operation.