If we found a sequence of DNA on some sample, and another identical sequence in that same sample, we still wouldn't know replication is happening.

However there may be slightly more requirements like the sequence has to be found in an oil film (bubble) up until it can form a skin/membrane, to protect itself, so even if it was happening on earth trillions of times every day no one would be there to discover it, and other life on the planet with a head start (bacteria, etc) would consume it before it made more 'progress' by evolution.

In the early planet there was nothing to "eat up" life as it was starting. Everything was on an equal footing.

There's strong evidence that all life on this planet can trace back to a single strand of DNA, which evolved exactly once in our billions of years.

For example, if I understand this correctly, a random jumble of DNA as you describe would have a 50/50 chance of twisting to the right or twisting to the left. And yet all life on earth uses DNA that is "right handed" twisting to the right.

The fact that life is right-hand twist DNA probably means left-hand was unsuccessful due to chemistry either in itself or in the environment, because an inversion of a molecule (chirality, twist, etc) means it will behave completely differently chemically. So left-hand twist can exist, but not necessarily in a way that can build life...even if it's able to initially replicate.

No. Oxygen screws a lot of things up. Also, RNAses are now everywhere (organisms secrete them all the time, which is why RNAse away is a product), and since the original replicating molecules were likely RNA, pretty much the entire world is toxic now.