Fertilizer requires the production of ammonia NH4. That is one nitrogen bonded to 4 hydrogens. The nitrogen can come from the air but the hydrogen has to come from some other compound.
That would be highly endothermic. The energy needed to separate the hydrogen from the water has to come from somewhere. If you meant "why can't we electrolyse that water to get the hydrogen", well yes of course that could be done, and that's what's being talked about (using water from some other source, though; why from the air?) But the water doesn't just decompose on its own.
You can, but doing so with renewable power would be under the rubric of "solving green hydrogen for industrial processes". In practice it's probably just easier to use renewably powered electrolysis to separate hydrogen and oxygen atoms from liquid water rather than try and use some chemical process to pull them out of the air.
Not dumb at all. Well, not exactly air, but that's how it's done. Air doesn't contain enough water, so you need to add some.
Currently nearly all ammonia is produced by "steam reformation" of methane in air (which is mainly nitrogen). Very hot steam, air, and methane are mixed. The carbon in the methane is released as carbon dioxide.
The idea is to take the methane out of the process.