BRUUUUUHHHHHH

Ah, so those designs which you can't get then was something everyone had?

You could either send off for books or dial up their BBS to get info, it wasn't secret at all. As a chip vendor you generally want people to use your chips, and even today most chips are still well documented publicly. Some vendors even give you free samples and all you have to do is ask. I sent off for all the free shit I could when I was a teenager in the 90s, and had piles of books and datasheets. To write an OS or a BIOS you don't need to know how the chip is designed the level you would to clone the chip, you just need a programmer's manual that tells you the higher level workings.

8-bit microprocessors were nothing particularly exotic when the 8088 (there was no 8084) was used by IBM in the PC. It was IBM's extremely low-end offering (so low end they didn't even use the 8086 with the 16 bit ext bus), that while still expensive set a new price point for low-end workstations. There were plenty of 8086/8088 copies, AMD was a second source, and I believe NEC got sued over the pin and instruction compatible V20. This was all by the mid 80s, and yes the Soviets had clones by then too, at the very least of the 8080, 8085, and Z80.

As far as what exactly was cloned and by whom, you're thinking of Compaq doing clean-room reverse engineering of IBM's BIOS so as to make a PC-compatible and pretty much spawning what we know as "PCs" today. Microsoft didn't have anything to do with that other than theirs ran the same DOS genuine IBMs did. Clean-room reversing a 1980s BIOS is more than feasible, they're not complex.

My username is related.