- God as creator. Did the universe just come about, or is there an intelligent designer behind it? (I'm not talking about 6-day creation specifically here.) This question is hard to resolve logically. On one hand, you have science that seems to make further and further progress answering questions that were previously just "God made it that way." On the other hand, however far the mechanisms get discovered, there are always more questions behind them of how things got to that point in the first place. And then there's the meta question of why anything exists at all (including either God or eternal inflation or whatever else).
- God who interacts. Is there some all-powerful, intelligent being who maintains active involvement with the universe and especially with people. Some entity that understands our language and can alter the natural course of events or, in some perspectives, maintain them. If I pray, can God enlighten me? Can God heal an illness or part the Red Sea? For many, this is an individual question who feel God's influence. My understanding is that some research exists on how people who pray or meditate or participate in church actively or other social groups might outlive or be happier than those that don't. That's vague enough, I'm not sure what can be said specifically on this matter based on research. Some believe they've seen miracles in their life. Some would say it's post-hoc analysis or selective attention. Also, if God is active and for some reason wants to stay hidden from scientific inquiry, could this being purposely choose only to be active in ways that aren't easily investigated? Maybe with occasional Red Sea partings or highly witnessed resurrections? (I reference Christian themes best because I know them best, but there might be others to consider.) And is it possible that God leaves memories of himself in us for delayed interaction. That is, do we interact with God's imprint rather than using some underlying faster-than-light universe-spanning interaction? Or if God does interact, does this being care about whether we are happy or not?
- God who defines right and wrong. There's no inherent meaning in objective science. Certain behaviors might lead to happier people or animals or plants or whatever, but who says people matter anyway? We could be coincidentally here, and if earth gets destroyed and we all die, oh well. So, what does it matter if we all kill and abuse each other to begin with? We don't want to do that too much, if social coordination promotes propagation, but it doesn't affect things being inherently right or wrong. If there are really such things are right and wrong, then there's some unchanging standard at the core of existence on which to base things.
Also, I'm sure that folks more familiar with classical theology or philosophy (from any part of the world) probably know more official terms for all of this. I'm not well versed in such things.