This is not and was never supposed to increase American research productivity. Just the opposite actually, they want less science done in America, and as a bonus they “save” about $5 billion, that is, approximately one half the cost of a single aircraft carrier
I mentioned Chesterton's Fence in another post here, about really understanding a problem and why things are done in a certain way, before tearing everything down. I'd really encourage people to try to understand things better before jumping to conclusions, it's not all that different from the engineer's disease that often gets mentioned on HN.
Facilites are the cost of buildings, electricity, janitorial service, etc. Think of this as things that might be included in the rent if you were renting a place to do the research.
Administration costs are mostly salaries for people, administrative and clerical staff. Not the people directly doing the research (that's a direct cost), but the people in charge of safety/compliance/legal, etc.
Administrative costs have been capped at 25% for a few decades. Facilities costs are not capped.