odds of it happening eventually, go up the longer you live.
Despite this DNA replication being highly controlled and very accurate, the sheer number of times it is performed in the lifespan of a person (estimated to be 10,000 trillion times!) means the introduction of a significant number of errors into the DNA of some of our cells from this fundamental process is inevitable. source
Yes. Your telomeres start to fray at the ends as you get older due to imperfect cell replications.
If we could solve that we’d be effectively immortal from death due to age related issues.
Telomere also don’t matter when replication enzymes add a random adenosine into a gene that controls genetic proofreading.