My understanding (of course it could easily be wrong, always verify this stuff) is that it's actively suppressed in the 'dormancy' stage, and it's more an almost inevitable failure of suppression that allows it to stop being 'dormant' so to speak.
Yes. It can take up to a decade for AIDS to develop after infection. The number of viral particles in the blood will peak shortly after infection, and it can cause flu-like symptoms for a week or so. And then the immune system will ramp up and it's almost fully suppressed. But some T4 cells have been hijacked and are spitting out HIV which is hijacking other T4 cells. This requires destroying the infected T4 cells. And a war of attrition and cumulative damage of a long inflammatory response eventually leads to increasing failure in that suppression. (Same caveats apply to my understanding.)