Your hopes all seem to be procedural, not related to policy. Which is fine, but ultimately the House is severely limited in what it can accomplish given the Senate and WH are in the hands of the opposition. The House can pass the most amazingly Conservative budget/bills in the history of Congress which will then die a very quick death in the Senate, and House Republicans will look like fools.
Conference committee's can negotiate rather than surrender.
House power is not limited to passing legislation, but also to serve as a block!
As for what I expect Jordan to accomplish, for starters, release ALL the J6 video which McCarthy promised, then reniged!
You are flat-out wrong about the last point.
Pass a stand-alone bill to fund Social Security and Medicare, and see what happens.
Then pass another one to fund the U.S. Dept. of Defense (with no funding for Ukraine), and see what happens.
Then work your way through each department of the U.S. government, one at a time.
You'd probably get through at least a dozen bills before you got to one that the U.S. Senate had the b@lls to reject.
What you're forgetting here is that the Senate and White House aren't the problem. The real problem is that we don't even have enough conservative Republicans in the HOUSE to pass a conservative budget/bill.