While my response is surely too late to be of any help, it's still a worthwhile conversation, in case others have similar problems with the lack of explicit motivation in the source material. I'll answer your questions with how I interpreted the setting:
What is it that he thinks Issrah wants and intends to do to Kovlar?
I think it's narratively more interesting if Chiselrock really has no idea what Ilssrah's true intentions are. He's aware of her affiliation with the Scarlet Triad, but beyond that I don't think he's clued into Droskar's Forge or Veshumerix or why he needed to smuggle the Antimagic Rune out of the vaults. She's just someone with a little bit of power and a complete lack of scruples, who can help him gain power in the Court by creating problems that Kelda can't solve but he can. I actually rather like your suggestion that Ilssrah can dangle the cultists as a potential poach.
There's a line in the description of the prison that suggests Chiselrock doesn't want to murder anyone inconvenient to his pursuits, which to me indicates he probably wouldn't be kosher with unleashing a dragon to destroy half the city and then bringing in Duergar to enslave the other half. I think he believes he's a good person with righteous goals and wouldn't sign up for the full conspiracy, but is motivated and hungry enough to eagerly swallow a lie about getting just a little quiet assistance climbing the political ladder in return for one tiny valuable object gathering dust in a vault.
How does he think he is going to come out of things looking like a hero?
I have a post slightly higher up on this very page that touches on this, but I think it makes sense that Chiselrock's vision involves him gathering a Dwarven crusade to march on Saggorak and liberate their ancestral homeland from the "evil" lich king. That's how he'd become a hero, the brave warrior who cut through the Court's red tape and finally took decisive and victorious action. Maybe they'd even rename it after him.
How exactly is he weakening the walls? And why would he want to weaken the walls?
I think your interpretation matched mine, which is also what I think is the most sensible read of the source: Droskar's Forge is what's quietly weakening the wall, nothing proactive on Chiselrock's part. His indifference about the wall's integrity could be chalked up to believing Ilssrah's found a way through and uses it to move herself and her agents into and out of Kovlar.