Can one half of the coconut be used for preparing the offerings for Perumal on one and can the other half of the coconut be used subsequently in cooking the next day and can it be offered to Perumal?

It is not a practice to use one half of coconut one day and the other half the next day to prepare offerings for Perumal. If we break a coconut, the entire coconut must be used on that day itself. If it cannot be used wholly, it can be used in other dishes after it has been offered to Perumal.
Notes
Certain households use one half of a coconut one day and the other half the next day and offer it to Perumal as one half is a separate coconut only. It is better to follow one’s household practice.