Pigeons nesting on ground?

Hi everyone! 

I recently made a post about a racing pigeon and a feral pigeon building a nest for each other outside my house where I could see them picking up sticks and happily moving them to a secluded spot on the side of a roof. 
However, a few days ago the female pigeon laid her first, then second egg but not in the nest! The pigeon laid the eggs on the ground. The area is secluded in the sense that it is surrounded by four walls so no other animals can get into the area however it is out in the open in the sense that it is not covered as there is no roof or anything when the pigeons are taking turns sat on the eggs. They also have been making a makeshift nest around the eggs but its not looking like a nest rather a pile of small sticks around the pigeon sitting on the eggs.
Firstly, I wanted to ask if this is common for pigeons? I’ve never seen a pigeon lay eggs before and certainly not on the concrete ground. 
Secondly, the weather is starting to get very cold and rainy so will this effect the pigeons as there is no cover over their makeshift nest so they will get wet. Does this mean they will abandon the eggs if it is too cold/wet? 
My final question is about the chicks (writing this I’ve realised I don’t know the word for baby pigeon!) if they are not hatched in a nest will they just be sat on the ground? This might sound silly but I assumed birds laid eggs in nests for the protection of their babies so I’m worried about the chicks being on the ground. 

Thank you for reading!