You can do Vets, Tax, and Social Security advocacy now without a law license to one degree or another. Once you have the law license from California, even though you are in federal administrative practice, the Washington state bar may take a dim view of you opening an office and advertising as an attorney with only a California license. This is a very gray area if you intend to have a physical presence in Washington. Since you would be competing with Washington licensed lawyers in the same field, eventually you will be subject to to a UPL (unlicensed practice of law) referal to the state bar. So instead of being outside the box, you will be in the box unless you plan accordingly and do your due diligence to avoid such issues. But the issue arises all the time - one just needs to be aware how to avoid it.
Nope each and every federal court and agency (if applicable) has its own rules. The good news is that DL degree holders who pass the Cal Bar can join many of them on motion.
You obviously have not attended law school, common sense and law are mutually exclusive.