Sorry to hear about your chicken but now you plan to pen the birds until they are bigger do you need to kill the cat? your neighbour has others so more will come, you cannot kill them all, just look at it as a learning curve prevention is better than a cure, perhaps you can build them a nice...
I take it they are being brooded by the parents? if so I would just leave them to it, it may or may not make it but if it has it's parents with it they may help a bit so it's best not to stress them by interfering especially if you are nervous, you may find it just hatches just fine.
If your quail are not securely penned expect a fox to get them one day, scaring and killing is no use when there is more than one fox in this world.....the sooner people begin to accept responsibility that their pens are not up to scratch when their livestock are killed the better.
I have my quail housed in two different runs with an upstairs bit really difficult to get into for eggs lol they don't lay quite as neatly as chickens and I thought I wasn't getting any eggs for the past week and then found a bunch of them hidden neatly in some conifer that I had put in there...
Sounds normal to me! I go through this routine pretty much every morning with my 3 girls and they are just hybrids lol! I can't do anything out there if they are out, all 3 of them want a piece of the action! I have quail too and a cat how old is she? mine were born last Nov so still youngsters...
The two larger ones are male but it would help if we can get a chest shot of the smaller one to confirm as it is difficult without seeing the breast feathers on a younger quail.
Yes it sounds like an accident rather than an act of aggression, chickens are heavy flyers and cannot manoeuvre themselves well, I take it she didn't continue to attack you on the ground and hasn't attacked anyone before?
Are you sure she hasn't gone broody? they say RIR are unlikely to go broody but I had an older RIR that went broody fairly regularly, quite annoying really as I wanted eggs and my others kept doing it too lol! give her an egg and see what she does, if she immediately shoves it under her and sits...
Did you hatch the eggs yourself or purchase the chicks/eggs from someone? personally if it was my chick I would put it down and look into getting the eggs or chicks from a different supplier if you got them from someone and let them know, they may give you a refund, as you say being a Cornish...