1. Smoking can be inimical(=harmful) to health.
  2. Board’s decision should not be inimical(=not friendly) to the interest of bottom-line shareholders.
  3. The states can be secular, but that should not be inimical to religious freedom.
  4. In her fits of delirium, nothing she mumbled(=said) made any sense.
  5. He sank(=fell) into a deep coma after suffering a stroke for the past two weeks.
    Please correct all.

I rarely use inimical myself. To me, #1 sounds a little odd, but 2 and 3 sound ok

4 is definitely fine. 5 should be “He has sunk into a deep coma for the past two weeks after suffering a stroke.”