“Have atheists ever heard of old age creationism?”
I do believe you meant old Earth creationism. Yes, we have heard of it.
“it's (sic) an Idea that God extending the time periods between days allowing life to exist over long period of time before the modern day. Think of an extinction event as being a creation of a new day (sic)”
It is called clutching at straws. You take what is shown to be fact by overwhelming evidence, i.e. evolution, and try to twist your myth, i.e. Genesis, to be more accommodating to the facts.
The pope believes that evolution and genesis (sic) can coexist (sic)”
I have never heard or read the opinions of the current pope on evolution. I think you will find that Pius XII said it supported evolution. I think John Paul II was more inclined to accept evolution but still made the claim “god did it”.
“I'm a YEC but most people today can't believe all things Romans 14 (sic)”
There is no evidence for a young Earth. In fact the evidence tells us the Earth is about 4.5 thousand million years old. Similarly, creation myths (and there are many) are not supported by any evidence. However, evolution is supported by more evidence than probably anything. I do not know what it says in Romans 14 without reading it. I am not inclined to read a chapter of a Biblical book to be able to address this question.
“Would you still give God (sic) a chance if it offer (sic) hope and the promise of eternal life (sic)”
If any god existed I would be, at least, be prepared to listen. I do not much care for the idea of living for ever. I think knowing you have a limit gives you a sense of purpose to get things done. I might be interested in eternity if it meant I could read everything I want to read but probably will never get around to reading. It is a nice idea if it means I will have time to visit all the places I would love to see. But, alas the religious tell us it would be an eternity of singing god’s praises. That holds no appeal for me.