I'm a bit confused about how I should approach those three. I know what they are but my problem is with cooking them.

Should quail be cooked to medium or medium rare like duck or should it be cooked liked chicken until it's no longer pink ? do you think quail will response well to braising or other slow cooking method ? or is it more suited to quick methods ?

The same questions above I have for Pigeons and Squabs what is the best way to approach them in your opinion ?

All birds that can actually fly will have breasts that can cook like duck breast or red meat. However, the larger birds like pigeon and pheasant will have legs that require braising to tenderize their meat, hence best to separate legs from breasts and cook them accordingly.

Quail can go either way as their legs stay tender when roasted, and breasts can handle braising. However, the legs need to be cooked through otherwise they are chewy, often resulting in breasts also cooked through. You can, of course, separate the legs from these tiny birds, or protect the breasts with some very cold bacon rasher (semi-frozen) during the roasting.

Last night I Bought 6 tiny quail , brined and air dried, roasted- couldn't find the meat, just lots of bones. The broiled chicken liver & Foie Gras Canapés were fantastic and new favorite but I need a bigger bird. Any suggestions?Stuffed them with butter and shallots which would have been amazing if there was some meat. The rest I'm gonna SousVide (in my Meile steam oven) @ 140 for 40 minutes cause I'm sure they can't be more than 1/4 " anywhere.
Quails are 4.5 oz (136 G) each. Are they usually that small?
Perfect chihuahua size, RAW of course. Now they can eat as good as us!

Thanks alot Tony and yes I did actually notice the chewiness in the undercooked legs.