I started a related thread but forgot to ask this question before I could edit it.
My questions are :
1> Life started from amino-acids. At what point since the beginning of life (as and if we understand it) did life forms started having DNA ? Or do we believe that life = DNA and DNA was there in the first living organism ?
2> What is the smallest feasible DNA molecule ? Thermodynamically, whats the temperature needed for this molecule to exist in the ppm level ?
See my answer to your other thread. [The threads ought to be merged.]
It depends what you count as a DNA molecule. I guess, with a permissive enough definition, it could be just two nucleotides, but that would not be a molecule with particularly interesting properties, not remotely enough for life.
I do not know specifically about the temperature issue, but large (and small) DNA molecules, and solutions of DNA at various concentrations, can exist quite happily at ordinary room temperature (and a good range above and below).
IANAB -
Since we don’t have any surviving examples of the earliest molecules, it’s hard to say. Without specific examples, how can you say something is “alive” or not? Is a virus “alive”? We obviously consider single-cell organisms as “alive”.
The power of RNA and DNA is that the molecules can be “self-replicating” with the correct mix of raw materials (amino acids, etc.?) and thus grow or reproduce. Since a DNA is a spiral of paired molecules, what is the cut-off? one of G/A/T/C? A pair? 4-plex? is DNA converted to “alive” when it manages to wrap itself in a protective coating?
It’s all quite speculative I think, but my understanding is that scientists conjecture that (RNA+Protein) life preceded the (DNA+Protein) life which eventually “won,” and that (RNA only) life may have existed before (RNA+Protein) life. A chain molecule (“AEG” ?) related to DNA or RNA but simpler (described in this pdf), and found in some blue-green algae has recently been hypothesized to have preceded RNA, though without, AFAICT, any evidence.
Some think TNA may have preceded RNA and DNA. Inevitably it all pretty much speculation, though. You are not going to find fossils.
And even beyond TNA, some think PNA was the first replicator. As the article mentions, the A is a misnomer.
So is the N, unless it’s actually found in cell nucleii. 
I guess I thought that the nucleobases would cover that part.
If you’re interested in learning about modern theories of abiogenesis, I recommend this series of lectures. It covers really nicely the various ideas that are out there right now, along with covering what evidence there is for each of them.
Thank you for the link - It looks like a great lecture and just what I was looking for. I will try getting it from the library, if I don’t get it there - then I’ll buy it. It seems most libraries have stopped doing Interlibrary Loans of A/V material.
Proteins can also be self-replicating but aren’t in any sense alive - take prions for example. Granted they only converted the correctly folded version of a protein to the prion version, but it’s still replication of a sort. However I did some digging and came up with this paper in Nature from 1996.