Why is only a tiny subset of these mutations passed onto our children?

Only major mutations of the DNA can be passed down to the next generation, this is because only those that affects the phenotype of the DNA gets passed on. Phenotype is the traits that can be observed in an organism using their genetic code. Many mutations occur on DNA part that serves no function this is why the subset is not passed on.

The answer to this will be from your lab notes/procedure. it would be best to ask another student who participated in the lab as we do not know what was done, what enzyme or if the temperature is celsius or fahrenheit. if i were to guess though i'd say the rate stopped due to enzyme denturing at high temperature

The basic building blocks of dna and rna are nucleotides