The introduction of the first citation explains it a little bit:

> DNA has limited chemical stability and decays without the enzymatic repair mechanisms of living cells [18]. Following cell death, nucleases start to cleave the DNA into fragments [19] and during decomposition, the DNA is digested by micro-organisms [18,20]. In determining long-term DNA decay, it is believed that hydrolysis of amino groups accelerates the loss of purine residues (depurination), resulting in strand cleavage [21,22]. This random DNA fragmentation generates a characteristic negative exponential correlation between DNA fragment length and number of molecules (figure 1a) [23,24,26,27].

This link might help answer your questions. Also, half-life in this context is just referring to how long it takes the number phosphodiesterase linkages (bonds holding the DNA backbone together) to decrease by 1/2. Half-life can refer to other types of decay as well :-)

https://www.nature.com/news/dna-has-a-521-year-half-life-1.1...

DNA has a half life, but the real question here is how being trapped in amber would affect that half life. So there may be more - or less - than one would expect if the DNA would be in some other environment. At a guess the time span involved is long enough that no matter how this would be influenced there still would not be any usable DNA fragments.

Everything has a half-life. Even plain old protons have a theoretical half-life of of 10^31 to 10^36 years.

https://en.wikipedia.org/wiki/Proton_decay

All exponential decay processes have half-lifes - or rather, half-life is a metric that describes the scale of an exponential decay rate.

https://en.wikipedia.org/wiki/Exponential_decay

It really depends; entropy is a harsh mistress. The output of a paper shredder can theoretically be reformed into the source paper, but below a certain size fragment there's not enough information left to recover.