I’m not Bible scholar, but this is what I think. Another poster has mentioned this idea, as well, so I’m not being original. If you look at the context of Romans 5, the passage is contrasting the first Adam with the Second Adam, Jesus. In the context of that argument, it doesn’t make sense to talk about the first Eve. The passage is not denying her existence or involvement, it’s just not mentioning her because she’s not pertinent to the point the writer is making.
The verse in Romans 3 is in a section that is talking about how everyone, Jew and Gentile, is in need of salvation - everyone needs the grace that is only available through Christ, and keeping the law isn’t enough. Could Mary be excluded from that ‘everyone’? She * could*. Personally I think it’s unlikely, because the whole passage is about the universal need for salvation through faith in Jesus.
Well, God the Holy Spirit dwells in believers, too (1 Corinthians 6 v19, for example. God hates sin, but He is willing and able to live in us, and work through us, even though we still sin. How does that work? I have no idea. For me, this is part of the mystery of the Incarnation. God was willing and able to become a baby, and be born of an ordinary, human mother. (Yes, OK, so Mary was extraordinary in terms of her obedience and love for God, but I hope you can see what I’m saying…) For Jesus to be fully human, he had to be born as we are all born, to imperfect, human parents. If Mary were this sinless, perfect person, that would hardly make for a normal upbringing, would it?

All through the Bible, we see God do extraordinary things through ordinary, flawed people. King David the adulterer; S/Paul, the persecutor of the faithful… why does Mary have to be any different?
Scripture isn’t always cut and dried, no. If it were, we would all agree on every point, and this forum would be pretty quiet. lol
I think you are right about what the non-Catholic answer to this is. Often, we can’t be sure. Learned theologians spend lifetimes discussing and debating some of these questions, precisely because it is so hard to know for sure. We non-Catholics learn to live with a degree of uncertainty about things. Perhaps Catholics do too? You’ll have to tell me. God is so far above us, we can’t expect to know and understand everything about Him and His ways. I trust that God will tell me if I’m seriously off track, and I pray that I’ll listen.