Not if this really is well-described by independent probabilities, i.e., a chance of being preserved that falls exponentially in time. Even if after 1 million years only half of the strands of DNA have had all their info destroyed, and even if (very unrealistically), the ones that haven't been destroyed are completely intact, then after 100 million years you would need to start with 2^100 = 10^30 DNA strands to have a single one last. And there are < 10^18 cells in a land animal.
No, the only way for something to survive is if the half life model breaks down and the chance of decay during different time periods isn't independent. This would be the case if one of the strands was somehow preserved accidentally.
Why would this be an exponential process? The error is per base pair per unit time. If a DNA fragment is split cleanly in half, each half should have double the expected time to failure as the whole, because there is half the number of base pairs each with the same likelihood of error as before.
It's just like nuclear atomic decay. For each base pair, there is a small chance of decay each small time step. The chance of any given base pair remaining undecayed through some time T is the product of all those probabilities, which fall exponentially in T. The expected number of total surviving base pair is also exponentially falling.
People are talking about two different things in this thread, and that's why people are talking past each other. Some people think halving means "half the number of base pairs remain" which would be an exponential process, yes. The other group thinks that "halving" means literally cut in half -- a failed base pair cuts the DNA strand into two pieces. That would be a linear decay process. As someone with no understanding of the underlying decay processes it's not obvious to me which one is right.
Yes, but you need fragments of only about 50 basepairs to assemble a genome (or a big part of it) back. A typical DNA strand has on the order of hundreds of millions of basepairs.
No, the only way for something to survive is if the half life model breaks down and the chance of decay during different time periods isn't independent. This would be the case if one of the strands was somehow preserved accidentally.