1. DIO could activate a THOUGHT BASED time stop before the effects of a Passive Aura, which he is already encompassed by at the start of the match, can affect him
2. That while in Time Stop, DIO could essentially walk and sit into a Disintegrator beam and wouldn't be harm
I mean, he could, Beyond is still a thing at the end of the day, Beyond straight up makes it so things that would kill or be lethal, just aren't for no real reason beyond just "it just isnt", a decent example would be when
Vampire Dio went out into the sun, something that instantly vaporizes him on contact by merely being in its presence, failed to actually disintegrate him because he wasn't allowed to die so he could act in broad daylight despite it being normally impossible for his kind.
And for 2, honestly?
It depends on how the beam does it, every single one of you aren't asking the right questions when it comes to shit working in stopped time, you're thinking in black and white terms when it's not actually that simple, the deciding factor is whether or not the things in question effect Dio under their own actions or if they effect Dio under things innately true for himself. If that disintegrator beam is stopped it can't really disintegrate anything depending how it does, does the beam work by rending the atoms apart itself? If so then yeah no, it wouldn't work, it's frozen so it can't actually perform the act of doing that, it's like, imagine picking up a HF blade from Metal Gear by the edge in stopped time, yeah sure it has quantum durahax on contact, but it's done under its own merit and by actions that are halted within stopped time, under the effects of stopped time, it's just a normal blade.
Another way to visualize this using basic concepts that in JoJo itself, imagine if Dio walked through flames within stopped time, he'd be fine as the transfer of heat is done under the flame's actions, not Dio's, the flames themselves are halted, they can't apply heat, transfer it or apply the effects beyond what how it was upon freezing, but if he walked through Hamon in stopped time, it'd effect him, not because Hamon works in stopped time but as it's his own body that reacts violently to the energy form itself regardless of what the Hamon is doing, for example.
If you all want to bicker back and forth about what can and can't work in time stop (not that it matters, match is rigged as **** anyhow), you should figure out how said abilities apply their effects onto a target in the first place, is it done under its own power? Well then no, it probably wouldn't effect anything in stopped time as the thing that applies the effect is halted, even if it is instantaneous, but is the effect something that's applied on the target's end? That Type 3 Madness example is actually a really good one imo, as that's a hax that works not on the end of the user, but on the end of the target, whether time is stopped or not, if the hax is done by you yourself perceiving it, then it's gonna work regardless of if the user can take action, as the action itself is done by you, not them.
So to answer the question, it's a case by case thing, literally just depends how it works.