Hello Nick,
First of all,Serialization is not part of OCPJP or
OCAJP exam, but it was part of OCPJP 6, so I think there is possibility of appearing partly Serialization related question in OCPJP-upgrade (1Z0-805) exam.
About API knowledge, No Nick you won't able to remember every little detail there, for certification or the real life. But you must remember the important and related API details related to exam objectives. For example, you will have to remember all API details of Comparator and Comparable interface for the exam objective "Use java.util.Comparator and java.lang.Comparable" as there are not much in API.
If you consider the exam objective "Format dates, numbers, and currency values for localization with the NumberFormat and DateFormat classes (including number format
patterns)" it will be really hard to remember all API details. In such a case
you should try to remember API details which related to exam objective and also you can understand what method does from its name. And be careful to remember if any important method throws checked exception or not as it may be tested in the real exam (In our simulator questions, we do check this too ).
I would suggest you to use short notes or flash card for this.
Hope you find this reply helpful and if any more doubts, we are here to clear.