They looked and saw Rosalind Franklin's X-ray crystallography which sparked them to think about the double-helix structure, and from there, they played around with cafeteria items (forks and spoons and whatnot) to create a model that finally worked.
A Mutation in one of an individual's somatic cells will not be passed onto the offspring.
The vaccine that may be administered to him at 14 years old is a dose of tetanus toxoid as this can present as pain from injection site. Since there is nothing said about the number of doses that he received, the patient should receive Tdap (tetanus, diphteria, and acellular pertussis) as stated from the Center of Disease Control and Prevention guideline for tetanus.