First a word of warning, getting Buddhists to agree can be like herding cats. We have had 2,500 years to disagree with each other, and there are a lot
of different sects with different beliefs.
(Origin question): How do you describe the origin of the human race and the world?
The universe has always existed. It has different parts, though none of the parts are permanent. The current material part (the STEM universe of science) started about 13.5 billion years ago as science describes.
The human race as we have it started about 250,000 years ago or so. Buddhism believe in reincarnation, to the chain of reincarnating lives goes back a lot further:
At Savatthi. There the Blessed One said: "From an inconstruable beginning comes transmigration. A beginning point is not evident, though beings hindered by ignorance and fettered by craving are transmigrating and wandering on."
-- Assu sutta, Samyutta Nikaya 15.3
(Identity question): Who are “we” as the human race? Are we an accident? Do we have intrinsic value?
All living things have some intrinsic value, including animals. Just as well since you can be reincarnated as an animal. Humans per se
are not unique because intelligent beings live on other planets in the Buddhist universe. The ancient Indians worked out that stars were very distant suns complete with their own earths, moons and planets. We are not an accident, see karma below.
(Meaning/purpose question): What is the meaning and purpose of life?
The meaning of life is that we all failed to attain nirvana in our last life, so we had better work to attain it during our current life if we do not want to be born again and die again. The purpose is what we choose to give it, wise or unwise.
(Morality question): Where does the idea of right and wrong come from?
Basically, "By their fruits shall you know them." Wise actions result in good karma and pleasant outcomes. Unwise actions result in bad karma and unpleasant outcomes. Buddhism does not have the concept of sin, just wise actions and unwise actions. Without sin there is no forgiveness of sin either, if you do the crime then karma ensures that you will do the time. Hence the need to think carefully before you act.
(Destiny question): What do you think happens to people after they die? Do you believe in heaven and hell? Who decides or how does one get to heaven versus hell?
Heavens (plural) and hells (plural). All are temporary, you do a lifetime on one of the other then get reborn again. After death you are reborn as something else: human, animal, alien, in a heaven or in a hell.
Your accumulated actions from your current and previous lives determine your next destination.
The exception is if you attained nirvana before you died, then you are not reborn. Nirvana is not one of the heavens. The Buddha attained nirvana at age 35. He died age 80. For 45 years he was living in the same world as his contemporaries while also being in nirvana.
Apologetic Action Questions:
What is your opinion of Christians in general?
How long is a piece of string? Some are nice, a few very much so. Others are not nice. Most are average.
If a Christian were to sit down and talk with you about their faith, what would it take to convince you that it was worth looking into or accepting?
Very difficult. I converted from Christianity to Buddhism in my teens so I've been there and done that. Christianity relies too much on God doing things for me, and I am not certain that God exists as described. Buddhism relies on my own actions, and I am a lot more certain that I exist than I am that God exists. Buddhist morality is effectively the same; the difference is meditation, which is very effective, more so than any Christian equivalents I have come across.
"Love others as you love yourself." -- Bhadramayakaravyakarana sutra 91
Thank you for some worthwhile questions.