As for the sound, I don't think Yamaha's implementation of "FM" [1] has been comprehensively reverse-engineered in the way that, say, the Commodore SID has. There are a lot of little quirks and edge cases to take into account when considering the full operational ranges of the various chips. Even MAME's implementation is allegedly distinguishable even after 20 years of tweaking and testing against hundreds of games, and I imagine most VSTs are using significantly less mature code.

[1] I recall reading that the actual implementation is phase modulation because directly doing FM in the digital domain would put quantization error in the frequency domain, i.e. notes would be off-pitch instead of having noise.

OTOH the things that tend to differentiate implementations of Yamaha's FM are the sample rates, bit depths, and envelopes used, plus any output distortion(YM2612 for example has a well known distortion in its implementation that adds a harsher edge). The core algorithms they use are something a high school student could pick up and do something with, and emulation quality issues are more a matter of it being easy to write an emulation that gets it 98% correct without covering the last steps, since those are details that really need error-for-error reproduction of the original ASICs and boards, including any timing issues - things which frustrate emulator writers everywhere.

Dedicated circuits.

This isn't all in CPU - the CPU on these synths mainly sets parameters for the sound generating chips.

not the same chips, but something like this probably:

https://en.wikipedia.org/wiki/Sound_chip#Yamaha_2

The SY99/77 really are great, though. I sold my TG77 and FS1R recently, but will probably get myself a used SY99 keyboard at some point. Or save up for a Montage.