To get this out of the way: I'm not a doctor nor do I play one - please take everything with a grain of salt.
You are most likely not vaccinated against everything as a kid (why should you - for example against tropical diseases) however when you visit certain coutries as an adult (or kid) you should or need in certain cases get vaccinated before you enter.
NB: I'm going to steer clear of addressing the specific scenario and stick to the general case, your friend should of course seek advice from their primary doctor regarding the best thing to do for the child in question.
Are there vaccines which specifically must not be taken too often, say after 5 years instead of 10 years?
Yes, for example REVAXIS - the ...
When a cat (or any other mammal) displays the symptoms of rabies (and biting with no reason is one of the symptoms), it dies within 10 days. No exception.
If the cat is infected, but does not display the symptoms, it can't infect any other animal, or yourself.
Conclusion: if the cat is still alive after 12 days, there is no reason why you should be infected.