I mean claims data, which is arguably a good record of your present health care intersections while employed at that company. They definitely have access to it.
They do not have access to claims data. They know your plan and your dependents, but that's it.
Yes they do if they are self insured, meaning they are literally the insurance company taking on the risk. This is the norm for large companies.
Where is the goal post? And no even they wouldn't have individual data, even if they self-insured. They don't manage the claims themselves, that's ridiculous.
Do you have any source for your suggestions, or is this just a random hypothetical?