Hi, Mian Zhiang:
In general, Holacracy gives you a way for every one in the company to sense problems/opportunities and participate in the evolution of the company. Required changes will be introduced by whomever senses the tension in the company and the evolution continues from there, again by the collective effort from everyone in the company.
How one company running Holacracy solves a tension will be different from the way other companies running Holacracy solve the same tension, but the solution will be "perfectly" adapted to each company's situation and context at any given moment in time.
Keeping this in mind, almost all of your question can be answered with "whatever way suits your environment, context, and tensions"
1. Holacracy does not prescribe how you should structure your circles, only that the natural groupings are called circles. You can, if you want or need, have an HR circle functioning in whiechever way the team thinks is best for the organization.
Having said that, there is a suggestion that you create roles, and therefore circles, that have "High Cohesion and Low Coupling". Having a centralized HR circle, depending on what it does, may have high coupling with other circles in the system.
in our company, and I believe in a lot of others as well, we have a People Circle, whose purpose is to supply the organization with a healthy pool of People available to fill roles. This is somewhat like an HR function in service of the needs of all the other circles, including itself.
Perhaps you've noticed that in some of the Self Managed/Organized companies, they do without centralized functions and just embed all these functions into the circles themselves. This is an approach geared toward higher agility and responsiveness, not necesarily for efficiency sake.
I'm in he higher agility camp, and would keep evolving our organization to achieve this eventually. For those more concern about efficiency, I don't think Holacracy prevents you from doing that.
2. "Whichever way suits your needs and environments" Each company is supposed to evolve their own practices to cover questions like these. However, the more organization experiment with different ways, the more models we can copy from. Currently, there are people who does the same exact thing they do prior to Holacracy with regards to hiring, firing, promotion, recognition. There are some that switch to advocate based compensation and termination. H1 uses badge based compensation.
You can adopt one of these models and evolve it further from there.
3. "Whichever way suits your needs and environment"
No, seriously, it really depends on what's best for your organization, and perhaps, trying out diffeent models and then sticking with the one you find most suitable is the best way.
We don't do anything special in our organization.
People fill multi-roles and are generally overloaded Because of this things get dropped, but we try to always drop the ones with lowest priorities.
If people reject a role fill request, which doesn't happen very often, the Lead Link finds someone else.
Some in this forum are experimenting with Attention Points, and some even trigger a request for hiring when, say, the total Attention Points exceed the Cumulative Attention Point threshold of the circle.
There are organizations experimenting with different and novel approaches to solve the questions you ask, and more. The Holacracy App Store captures some of these approaches to be used by others having the same problem.
Hope this helps