P24 is no longer able to be detected when antibody production starts and it can take up to 3 months for there to be enough antibodies for the antibody test to detect. Which is why you have already been told that a conclusive negative test is 3 months.
Correct. MOST people will test positive by six weeks. The three months waiting period is to catch the ones that did not produce enough antibodies at six weeks and by 3 months it is conclusive that if there is no antibodies detected at that time, the person is negative.