All spending must go through House of Reps.
Try running a government program without money.
It can be abolished one way or the other.
Don't be so sure. The EPA was created by executive order (Nixon) to administer laws enacted by Congress between 1955 and 1971, including but not limited to the Air Pollution Control Act, the Clean Air Act, the Water Quality Act, the Clean Waters Restoration Act, the Wild and Scenic Rivers Act, and the Endangered Species Act, among others.
The budget authority upon which the EPA relies is diffused among these various pieces of legislation, and a lot of it comes from fees and indirect (use) taxes.
I was very interested in how to structure a repeal Bill (I know, fat chance), but after careful study I realized that the EPA and its (alleged) powers are probably immune to Congressional interference, unless a future Congress repeals all the enabling legislation or a future Supreme Court rules that delegation of legislative power in an open-ended fashion is unconstitutional.
The EPA is a prototype of a post-constitutional governmental agency, seemingly created in a proper way but not really subject to control by elected officials.
Needless to say, it won't be the last without a major, major change - and I do not mean by "electing more Republicans".