Some processing ideas for a small bird:
https://www.backyardchickens.com/articles/how-to-process-your-quail-including-gory-pictures.75834/
Here is an article that talks about processing quail, with photos. It lists several methods. I see a photo with one finger reaching into the body cavity to...
Yes to all of those.
Some people butcher Coturnix Quail (adult live weight often about 6 ounces). If you are dealing with very small chickens, you might look for threads on butchering and cooking quail.
There can be shortcut processing methods that save time as compared with the "usual"...