I'm a medical school graduate student. However, I wish to apply for a PhD program in molecular and cell biology, I'm interested in understanding the interactions within and between cells at molecular level. However, it seems that at many programs, courses on physics and mathematics are required. I didn't take any mathematical or physical courses. Is it possible to take these courses without having to go through the whole bachelor's curriculum? If this is possible, how could I do this?
In the US it is not uncommon for universities to allow students to take individual courses without seeking a degree. This is especially true of some of the larger introductory type courses that are required for getting into grad school. It is probably worth contacting the schools you are interested in applying and telling them you have not taken all the prerequisite courses and if there is something that can be arranged.
Most of PhD projects in molecular and cell biology concentrate on experimental work and you will need to read a lot about other experimental works, results and conclusions, etc.
You may also need to read about structures and interactions but this will be similar to human anatomy and physiology you have already tried.
This is unlikely to be a problem for a medical graduate. I would say, go on.