I'm not sure anyone here has experience in designing and making chips it's dominated by only a few companies. My answers below are my best guesses based on what I think will be a useful starting point.
I don't think you'll get a good profitibility out of chips if you're just doing this hobbyistically - there's quite a bit of competition in this space imo and they probably have to compete quite well with each other already (some have stopped producing entirely too).
1) Is this even right place to ask such questions?
Kinda but you might want to ask it on more forums too or in communities where chips are designed.
3.2) Complicated functions of processors
3.3) How sha256 works indepths
The sha256 algorithm is the main function asic chips implement as weel as (probably) a comparison to check if the header is below the target - operations are normally done in parallel as much as possible afaik to increase the speed a block is found (this might be less necessary though as series processing over the same amount of time will produce a similar number of outputs for ~10 minute intervals).
3.4) How ASIC receives jobs
3.5) How mining pools work
Pools send jobs to computer workers that mine the blocks based on the information the pools give them.
These "workers" are pieces of software on a "normal" machine (ie one running Windows or Linux with the asics connected as peripherals) that deligate tasks to asics.
I think the APIs for these are quite well implemented though so you'd just have to look at integrating the asic chips with preexisting software to start with.
3.6) How USB miners work
This might be easier to work out by buying a cheap USB miner (or making one yourself out of a cheap device).
You could also look at software like cpuminer or check other crypto mining software that's open source.
3.8.) How to design an ASIC chip
You'll likely want to start off with the basis of a chip that can do sha256 algorithms and then work from there to add things.
