A. You're right that it's complicated (and as you know, one can never get a straight or simple answer from a professor).
Since mammalian sex is controlled chromosomally, then one could say that sex is determined once the sperm nucleus enters the egg (having either a Y or X chromosome). But really, there is no single point in development when sex is determined.
So-called 'primary sex determination' occurs in the gonads caused by the chromosomal difference - XX vs. XY. The bipotential gonad ('genital ridge') can be seen to look a bit different by about 7 weeks (obvious by 8 weeks), but, of course, gene expression has been different before that. Genes are saying both 'make testes' and 'don't make ovary' if the cells have a Y, and 'make ovary' and 'don't make testes' if there is no Y. [There is a single gene on the Y (SRY) that is generally sufficient to determine sex - if that gene is moved to an X chromosome, then an XX (+SRY) individual develops completely as a male with testes (although sterile, since the Y is needed to make sperm).]
When the testes vs. ovary secrete hormones, then all the other body tissues respond to generate male or female sexual characteristics ('secondary sex determination'). Except when it doesn't happen - such as in 'androgen insensitivity syndrome' when an individual with XY and testes (and male hormones) will develop otherwise almost completely female secondary characteristics. [During normal human embryonic development, in response to gonadal sex hormones, external genitalia become barely distinguishable at about the 10th week, and more obvious after the 3rd month.] The process is continuous, and to some extent reversible - as seen in sex reassignment hormone therapy. Some regression of secondary sexual characteristics can be seen in clinically defined 'hypodgonadism' when insufficient sex hormones are secreted, but also in normal conditions of aging and for women, after menopause. And development of 'binary' secondary sex characteristics is imperfect: intersex individuals having mixed or ambiguous sexual characteristics occur at a rate of 1 in 2000 to 1 in 4500 births.
Another early event that is related but not the same is X chromosome inactivation, which I believe in humans occurs around implantation. XX individuals permanently turn off one of their two X chromosomes at random. That way both XX and XY cells have the same level of X gene expression (the process is known as 'dosage compensation'); if it doesn't happen it's lethal for the embryo. But the subsequent expression of genes that tell the gonad to be male or female is an independent process.
On the NCBI bookshelf: Chromosomal sex determination in mammals - This is from an older edition of a standard developmental biology textbook (the one we use for 'Biology 376'). The basics remain the same, although we know a lot more about the genes involved now.
Another good source at the same site: Sex determination in mammals: coordinated control by the endocrine system