The next President, if someone Conservative with balls, could investigate and find Obababa to be illegally President and declare all laws/regs made under his authority to be null and void.
Which would be a quick Obababa Cr*pCare fix.
Among many other travesties.
No. As a general rule even if a public officer is later found to be ineligible to serve that doesn't void the official actions taken at the time.