Which statement is correct about the uterine cycle?

I would say that both (a) the menstrual phase of the cycle is from day 1 to day 8, and (d) if fertilization occurs, the corpus luteum is maintained by a hormone secreted by the developing embryo are both generally correct.

a) the menstrual phase of the cycle is from day 1 to day 8.

Most women count day 1 of their cycle from the first day of menstruation or bleeding. Bleeding lasts from 5 to 8 days.

From a scientific or medical perspective, the first phase of the menstrual cycle is the follicular or proliferative phase (which starts at around day 7 until day 14), followed by the secretory phase or luteal phase (which starts at around day 15 until day 28), and ending with the menstrual phase (which starts at day 1 until day 7 or 8).  However, even though the menstrual cycle is considered to be the last phase, doctors and scientists still say that it starts on day 1 of the cycle.

b) during the secretory phase, estrogen levels are at their highest.

Estrogen levels are lowest during the menstrual phase. Estrogen peaks just before ovulation, at around 13 days after the start of menstruation, during the proliferative phase, just BEFORE the start of the secretory phase.  And estrogen levels are medium during the secretory phase.

The secretory or luteal phase follows ovulation and lasts from about day 15 to day 28. After the follicle ruptures as it releases its egg, it forms a corpus luteum. During the secretory phase of the menstrual cycle, the hormone progesterone is produced by the ovaries and secreted by the corpus luteum. Progesterone secreted by the corpus luteum stimulates the further build-up of the cells in the endometrium of the uterus. Progesterone also stimulates the glands in the uterus to secrete substances that maintain the endometrium and keep it from breaking down. For this reason, this phase of the menstrual cycle is called the secretory phase.

c) during the proliferative phase, levels of progestorone rise as the follicle begins to produce more hormone.

Progesterone is produced mostly by the corpus luteum (which used to be the graafian follice but is no longer called by that name after ovulation).  Levels of progesterone rise, AFTER OVULATION, during the secretory phase.

During the proliferative phase the lining of the uterus is built up stimulated by ESTROGEN secreted by the ovaries. A surge of luteinising hormone stimulates the mature follicle in one of the ovaries to release its egg. The other follicles break down. Estrogen also peaks during this surge.

d) if fertilization occurs, the corpus luteum is maintained by a hormone secreted by the developing embryo

The corpus luteum is programmed to die in 14 days unless it receives stimulation from a hormone secreted from a growing embryo. This hormone is human chorionic gonadotropin (hCG). Under the control of hCG, the corpus luteum continues to secrete estrogen and progesterone throughout the pregnancy. Human chorionic gonadotropin (hCG) is made by the embryo soon after conception and LATER BY THE PLACENTA. Do you consider the placenta to be part of the developing embryo?)