I don't agree Billg as one of the most brilliant people of our time. He is certainly a clever strategist, but not much more than that. He got incredibly lucky a couple times: The non-exclusivity IBM deal, the PC clone market (that could have not existed if the BIOS were harder to reverse engineer - say, like a Mac). MS has also at least one failed attempts to create a PC-like environment: MSX. They saw that a commodity computer running an OS they controlled was a way to get big money.

I would also like to know if they somehow covertly helped the BIOS reverse engineering process.

Everything they did up to Windows 3 derived from that - do whatever it takes to secure a market for their OS. They did not leave OS/2 to IBM because the codebase was bad. They needed control of the OS in order to keep it a commodity and having a competitor developing the OS that runs on commodity PCs was out of the question. Up to the launch of Windows 3, the public discourse was that OS/2 was the future. It changed dramatically at that minute.

They played dirty tricks all the time. Threatening Apple not to renew the Applesoft BASIC license was a way to secure Apple would endorse Microsoft BASIC on the Mac and ditch a competing product. I don't know what else they got from Apple while their cash cow had a piece of MS software within. It certainly made Apple's contracts better the next time.

They got lucky a couple times and IBM got fooled twice. Their dominance is the consequence of luck and borderline criminal tactics. I see no huge genius here beyond one that was willing to bend the law (and morality) as much as he could.

It's also unclear how much of this came from Ballmer.

As far as I know, the big genius among the Microsoft founders is Paul Allen.