Racing Pigeon Nesting with Wild Pigeon

Hi!

I recent found this site while trying to research about racing pigeons. For the last week or so a racing pigeon (it has a green tag and 2 white tags on its legs) has been coming to my sitting room window as it faces a gutter where it drinks it’s water from. I read that it might be hungry and taking a break from racing so I put out some diced berries and oats for it to eat twice a day for two days. I realised that it was coming and happily eating with another bird that was not tagged. My knowledge of pigeons comes completely from simple google searches so I will call this non-tagged bird a wild pigeon sorry if that’s not enough detail. 
After putting this food out I did read that it’s best to stop feeding it to encourage it to go home so that’s exactly what I did. The two pigeons are inseparable and still a few days later sit on my window and peck at the glass for more food! It’s very cute I must say. 
This action has died off a bit since I guess they must know that there isn’t any more food however, I noticed the two birds courting doing what google says is a ‘pigeon kiss’. Again, very adorable! 
After a couple of days of flying back and forth between my window/gutter area and I’m guessing just generally around town they have started building a nest together! 
I see them hopping around picking up sticks and feathers and taking them over to a hidden area and coming back out for more. I guess this means that they are building a nest for incoming babies! 
All of this is very cute to me however I really just want to know if this is normal? Should a racing pigeon be mating and building a nest with a wild pigeon? Will the racing pigeon ever go home now? 

Thank you for reading!!