Hi Hman,
Good questions. There’s a lot to reply to here, and others have made some good points, but I also want to push back a bit on the idea that the age of the earth is somehow vital for “proper” theology. As you’ve alluded to, the Bible also implies that the earth is flat and the solar system is geocentric, and so perhaps the answer is that we should avoid reading the Bible as a science textbook, as if we were to expect it to communicate 21st-century scientific ideas, when the cultures it was written to were so incredibly different than ours.
The first few chapters of Genesis communicate some very important theological ideas to us: we are made in God’s image, we are made male and female, God created everything, the world is very good but has also been corrupted by sin (and therefore needs a redeemer in the person of Jesus), etc. I don’t see that any of these important ideas require the earth to be young. One of my major concerns about organizations such as Answers in Genesis (I grew up with their teachings and visited the creation museum as a young adult) is that they place an inordinate amount of importance on the age of the earth, to the point where they imply that the entire Christian faith stands or falls on such an issue. It does not – the foundation of the Christian faith is Jesus Christ and nothing else. His life, death, and resurrection are what we believe, confess, and follow, and while the Old Testament is important, I’d be wary of any organization that tries to convince people that the age of the earth is essential for Christian theology.