When does Andrew know he has AIDS?

Yes. He's receiving treatment in a clinic, surrounded by other AIDS patients in various stages of the disease. Calling his mother to update her on his T-cells and platelets is another indicator that he knows he has AIDS.

He had AIDS throughout the entire movie. It's not made absolutely clear how he got it. You may speculate that it was because of his sexual preferance, but it's never stated exactly how.

He knew he had it at the beginning of the movie. Hence the racquetball lie on his head.

Everyone here really answered this well. Yes, Andy already had the AIDS diagnosis. From the beginning of the film, Andy already has KS. We never learn when he first got diagnosed, but it was likely KS that lead to the official AIDS diagnosis and perhaps even first discovering he was even infected, although we do not know the background for certain. He tells his mother about good news in the blood work because he's poz (and not just poz, but has already progressed to AIDS). People's statuses that were unknown in the early 90s would never speak about "T-cells holding steady." The diagnostic tests were already available then, and T-cell counts have never been part of HIV confirmation, so when Andy speaks of T-cell counts, platelets, etc. it's because he already knew he was sick.

Edit: Someone in another thread said the trailer revealed when he was diagnosed, and they're right. "Eight months before" meeting with Joe for counsel (which is what? Two months after being fired?), Andy reveals the diagnosis came after a bout of pneumonia. So my guess of KS first was wrong.