I didn't say they were synonymous. Perhaps @Open Heart wrote that?In every verse you cite, a distinction is made between Israel and Judah. Why mention both if they are synonymous?
It is my view that Judah and Israel are one nation. A distinction is necessary for the same reason that Israel is comprised of 12 (or 13, depends how you count) tribes, which is that each tribe has unique qualities that make the whole better.