I think any breed a dog with half a nose and a will to hunt could be a good squirrel dog. Hardest thing to teach most of 'em is not to chew 'em up when they fall from the tree still kickin'. I made the mistake one day bird huntin' when the birds were absent, to shoot a coupla squirrels on the way back to the truck for supper. From that day on, my GWP couldn't walk by any large tree without stopping and looking up.
For turkeys, fall is when one would use a dog. In most states where it's legal to use dogs for turkeys, it's only legal in the fall. I use mine like overhead described. To scatter a flock so that one can use assembly calls to bring them back to the spot they were scattered from. This only works if the flock is scattered in more than one direction. You scatter the whole flock as one and they generally keep going and don't come back. Get even one or two to in a different direction and the whole flock will come back to the exact spot they were scattered from. Many times within just a few minutes. Dogs with their better speed get closer before the flush and tend to make the birds fly. When they fly, they tend to scatter better than when they just run. I also have shot turkeys from points from my bird dogs. If you ever wonder where those big birds go sometimes when they just seem to disappear, they are well adept at crouching down and disappearing under cover like a pheasant. When they bust tho, they bust like a giant grouse and just explode into the air. Sometimes if you get lucky, they stick their head up first. Surprisingly, every bird I have shot from behind a staunch point has been a mature tom.