US Agencies don't need a Constitutional Amendment to come into existence - the usual method is simply a law that Congress passes that the President then signs. E.g. Dept of Energy, Dept of Education, Dept of Homeland Security, Dept of Housing and Urban Development, etc. going way back to the Dept of Foreign Affairs (precursor to Dept of State).
Obamacare (Patient Protection and Affordable Care Act) was also created by Congress - bill passed in both houses, signed by the President, upheld by the Supreme Court. That's basically a textbook example of how the system is supposed to work.
I'm not sure why the EPA (and others, like FEMA) were created by Executive Order instead.
As far as why Congress hasn't declared war since WW2, they've basically rolled up their say into the War Powers Act and the War Powers Resolution which provides for them being informed and issuing continuing approvals. They can then support the President (as Commander in Chief) but not officially declare war.