I'm surprised a tiny change in genes doesn't completely destroy the viability of the organism. You can change one character in code and it no longer compiles or the entire thing crashes.
2) DNA has 2 matching strands. Basically, 2 copies of the same information. DNA constantly degrades and is constantly repaired with information from the other pair. You may think of it as RAID1.
3) We have 2 copies for almost all the genes. Some more than 2. Hemoglobin-alpha has 4 copies. For keratin we have 100+ functional genes (and more non-functional). [1] Think of it as data backups and versioning.
4) For some organism functions, more than one protein do the same job. For some metabolic pathways there are alternatives. It's like we have both GTK and QT working at the same time for any program, and some ancient TK and SDL remains form our ancerstors that could be used if all else fails.
5) The "program" can still crash. It's a miscarriage / spontaneous abortion. Try again with different versions of "libraries" and it will work.
[1] https://en.wikipedia.org/wiki/Keratin-associated_protein