Lefty / Happily Married / Parent of 2 Girls / Christian / Yucata User
Smack dat Ghoulie, Mr. Trolla!
Page 4 of the rulebook states (in section "Additional Rules"): If a god loses all of its Health Ringchips it goes from "standing" to "fallen". Turn the god on its side and place it on its hex on top of any dropped Armor Bonus or Attack Bonus Ringchips. (emphasis mine)
This would seem to indicate that both red & green chips would be returned to the supply. Only "Bonuses" stay in play.
Your 2nd question actually is a 2-part issue. #1: You can never heal/remove poison chips; you can only add/replace health chips. #2: If a god falls (and his green & red chips are removed from play), if he were to be re-animated/healed prior to your cleanup phase (using 1 or more of your actions) he would be rid of the poison.
AFAIK, the only time Poison stays in play is with the use of the "Cursed Kopesh" card from the Egyptian Expansion. Yet even there it is not the Ringchips but rather the capacity to inflict poison damage that remains in play.