In a grammatical sense, both are technically correct. However, if you are trying to use it to emphasize the humanity that you both share, it is more correct to say "He's made of flesh and blood, just like you and me." The other way of saying it, technically can be said, however, it isn't an expression we commonly use :) Hope this helps!

Depends on the context, but for the most part I would say yes.

Most people will know what you mean, but they're not the same. 'Flesh and bones' is more about solid structural materials (as opposed to intangible ideas & energetics); while 'flesh and blood' is more about humanity (as opposed to insensitive & inanimate objects).