I hope you will not find my reply too unsatisfactory. I haven't contributed to the forum before so I thought I would address a couple of issues your questions raise.
1. Explain the origin of all matter in the universe, and don't use the Big Bang. That is only what dispersed it.
I don't think you should answer a question which seeks to restrict your response in this way. One may as well ask, "Explain who Christ was, but don't mention God, He's just a metaphor."
Of course, there are cosmological theories as explained in other posts, but if neither you nor your questioner are experts in the field, you may find the debate sterile.
If you were questoning your creationist friend on the doctrine of the trinity (if they are trinitarian), would it be fair to expect them to be able to parse obscure hebrew verbs, interpret the rather difficult greek paleography of some fragments of John, balance historical interpretations of the Talmud or the Septuagint, or tackle the intricacies of the council of Nicea? And were you to consult experts, would the debate between you be fruitful or just a tennis match of quotations - with all the problems of misunderstanding and misquotation that would ensue?
In such we rely on authority - the teaching of pastor or church in theological matters, the teaching of scientists in scientific. Do not be abashed to say "The science is too difficult for me". There can be no harm in the position that we respect and believe the teachings and systematics of scientists and theologians alike because we can see the application of their work revealing palpable truth in other areas.
But perhaps the other questions are more fruitful for non-specialist debate, if not in their ecological and biological details, then in their principles.
2. Explain how a venus fly-trap evolved. "The trap required an idea."
This type of question presupposes a direction (in both senses) to the development of the fly-trap. By direction in both senses, I mean: directed by someone/thing and leading towards some state already defined as an end point before it is actually reached. Scientists of all varieties are prone to the latter use.
The confusion is simply because we take an anthropocentric view of the created world (or uncreated, if you prefer) and assume that means and ends are related as we would relate them.
I like the polar bear example: "the purpose of the bear's white fur is to camouflage it" is a handy anthropocentric shorthand for "bears with white fur survive when bears with coloured fur do not."
So the purpose of the fly-trap is to trap flies? No - the fly-trap just survives better.