Nope.
He was the president, validly or not.
As for what he signed, that depends.
If it's an executive order, it's gone as of 20 January.
If it's a law, then the new Congress must repeal or modify it.
As for the debt, the new Congress must pass laws to unleash economic growth and refrain from passing laws that increase the debt. If they that, and stick with it, then, over time, economic growth will retire the debt, and America will remain on top of the pack (because the others will lack the discipline).
No, if he is not eligible, then he was not the President. We didn't have one. Unless you like the idea of setting that precedent.
Odds are pretty good he didn't win that second election either.
He deserves neither SS protection, nor financial benefits, but rather court, lawsuits and at the very least, long term imprisonment.