Is it permissible to fulfill only the essential requests of parents when one is busy with studies and work, and to postpone other requests to a later time, especially if the parents ask for a lot and turn non-essential matters into essential ones, and do not consider the son's health or educational circumstances?

The rights of parents are great, and it is obligatory to honor them and obey them in what is good, unless obeying them would cause you harm, in which case obedience is not obligatory. There is no harm in continuing your studies alongside a profitable job, even if this conflicts with some of your parents' non-essential requests. You must strive to honor your parents, treat them kindly, and address them with respect, gentleness, and humility, for honoring them is one of the greatest causes for Allah's pleasure and entering Paradise.