Conceptual Questions on Self-Funded Coverage Question on Deductibles & General Health Insurance [AETNA HDHP with HSA]

Hi Reddit, I am new to self-funded coverage and kinda health insurance in general. After some research, I feel that I understood some parts but am still confused throughout. Self in this case refers to the employer self, not the employee self, which was kind of a confusing name from the perspective of the employee/insured. The dynamic of deductible and self-funded coverage was also a bit confusing for me.

How is a self-funded coverage funded? (I get that the employer funds the coverage by putting in a fix amount in a pool for the employees, but is that pool directly made up of the monthly “premium” the insured employee has to pay? [e.g., if the company has 500 employees enrolled in the HDHP plan, each paying $40 per month, is that a total $20000/month going into the pool, or is the pool made up by the employer through other means?])

What is covered? (It seemed that the employer selects what procedures etc. are covered as opposed to the health insurance company, so I’m assuming this answer has to come from the employer and differs by company, is that correct?)

How does deductible come into play with self-funded coverage, in both the scenario where a procedure is covered and where it is not? (In the covered scenario, does the employer use the fund to pay for the full cost of the procedure / doctor’s visit / etc. without the deductible kicking in? Or does the employer pay the remaining of what’s after the deductible? In the not-covered scenario, does the employer not use the fund to pay any cost at all, and the employee pays the full cost (including what’s after the deductible as well? Can you even perform a procedure that’s not covered in this case? Is this where the out-of-pocket maximum come into play? [whereas deductibles apply to covered procedures, out-of-pocket contributes to both covered and uncovered?])

How does the health insurance company come into play in keeping the cost down / negotiating in a self-funded coverage? Do they have a role at all here? In the case that an employer “covers” a procedure, will the insurance company still help negotiate the price down? What about when a employer chooses not to cover it, will the insurance company negotiate price down still?)

Is there anything that gets covered in general before deductible kicks in? (e.g., [some?] preventive care is covered without needing to pay that deductible, are there any other examples of such cases?)