If we do mention scientific discoveries when they in a certain way help to back up the truth of Torah, but refuse them when they go against it, how do we draw the line and reference of how to deal with science?

Listen, this is a very important question, and I want to make something clear from the outset: we don't need science to prove the Torah. The Torah is truth whether science agrees with it or not. Science is always catching up to the Torah, not the other way around. Now, when do we reference science? When science discovers something, we can show that the Torah already said it three thousand years ago. For example, when scientists recently discovered how many stars are in the universe, we can point out that this exact number already appears in Masechet Berachot page 32b. When they discovered information about DNA, about radiation, about the structure of creation - all of this is already in the Torah. We use these discoveries to show that the Torah possesses knowledge that no human being could have written at that time. But here's the key point you need to understand: when science seems to contradict the Torah, it means one of two things. Either the scientists are making a mistake - and believe me, they make plenty of mistakes, their theories change all the time - or we're not understanding the Torah correctly yet. The error is always on the human side, never in the Torah itself. The line we draw is simple: science is based on theories, which by definition means educated guesses. These guesses are constantly changing, constantly being revised. The Torah is divine fact. When scientists say the world is billions of years old, they're using dating systems that have major flaws. They themselves disagree with each other - one says sixty million years, another says two hundred million years. If your base measurement is a variable and keeps changing, you can't know anything for certain. Look, even with dinosaurs. The Torah talks about tanninim gedolim, these giant creatures. David HaMelech climbed what he thought was a mountain but was actually a dinosaur. The sages saw these creatures. So when science discovers dinosaur bones, they're not contradicting the Torah - they're finally catching up to what we already knew. The problem today is that people try to match the Torah to science instead of matching science to the Torah. They assume science is fact and Torah is theory, when it's exactly the opposite. This is backwards and dangerous thinking. Here's what you need to know: there has never been a scientific fact - not theory, but fact - that has proven the Torah wrong. Not once. Never. If someone claims they found such a thing, it's either based on theory, not fact, or they don't understand Torah, or they don't understand science, or both. The Rambam teaches us that when we contemplate Hashem's wondrous and great deeds and creations, we come to love and fear Him. If you're learning science to understand how Yaakov Avinu did what he did, how Moshe Rabbeinu performed miracles, how creation works according to Torah - then that science is going to make you appreciate Hashem more. But if you're learning science independent of Torah, or worse, against Torah, then it's not going to help you at all. So the reference point is always Torah. Torah is the measuring stick. Science has no authority over Torah. When science helps us see Hashem's fingerprints in creation, we use it. When scientists make claims that go against Torah, we know they're wrong, even if we don't yet understand exactly how. Eventually, science will correct itself. It always does.