For example, in this motherboard, doesn't the and boot off of a firmware in that amd chip?
No. It boots off the bios ROM in the lower right-hand corner.
An intel 8086 and all later variants will make copies of your stuff and leave it lying around in extra shift registers which can be useful for debugging and necessary for identification when on the internet. A lot of websites have been set up to do nothing until they have returns which were once upon a time mistakes or proprietary Intel circuits.
No. Sigh. FWIW, my PPC Mac still surfs the net just fine, as do ARM-based chromebooks, tablets, and cellphones and MIPS-based internet appliances of various sorts.
Unique identifiers inside of CPU chips are a comparatively recent feature (SW folk like microsoft like them for licensing and such.) Newer AVRs have internal unique identifiers as well.
The "Pentium Bug" is LONG over and gone... (wikipedia says "if your processor is at least 120MHz, you don't have the bug.") And "pentium", meaning it wasn't present in 8086, 80286, 80386, or 80486 (all 'later than an 8086.') (the first three didn't have floating point...)