The discussion about the feather made me curious: I've seen chicks swallow legs, do they eat other bones as well?
Actually when they try to eat feet they end up having to yak them up again (or have them removed by parent/sibling). That doesn't stop them from trying. Food gets stored in the crop until it passes on to the first of the falcon's two "stomachs". The legs tend to get caught at that part - think sword swallowing. They can eat bones, one of their stomachs I believe can dissolve they, but I don't believe they do it much or often on purpose.
And how do the parents prepare the meal for the chicks? Besides removing the feathers. 
Usually, food is "packaged" before it comes in. Head off, wings off, legs off as they aren't the edible parts (or not chick-edible parts, the adults do like brains). Often many or most of the feathers are removed as well. Makes it easier to carry food - a pigeon is big - easier to just carry the torso than the whole bird. Can mean larger meals come in - or rather more food per delivery. Trey was the master, Ivy was not so neat but delivered tons of food. This year Princess and Smiley have to pluck their meals in situ (hence the feathered nestbox). Hopefully Smiley will refine his technique as he gets more years and experience under his "belt".
