Maybe. Even today many doctors and private hospitals won't accept new Medicare patients due to the caps in the payment schedule. If you assume Medicare would have to accept anyone who wanted to buy in, irrespective of preexisting conditions, then it would have much more inherent risk. Which means higher costs or even lower payouts, making it even less desirable for health care providers.
Nope. Hand-in-hand with the individual mandate, a broader Medicare-as-public-option would end up having a lot of younger buyers. Plus, a lot of employers, especially smaller ones, would see Medicare as an attractive option as well, which will further improve risk pooling.
It doesn't have to be. Some plans push for a complete replacement of all private insurance. I see no reason for that to be the case. If you want to pay for expensive insurance that, say, has broader coverage, or more in-network hospitals, or other perks, you should be able to go for it. And such plans should be available for employers to buy as a perk they can offer to entice talent.
None of that is in conflict with a public option available to everyone else. This is literally what Obamacare was initially designed to look like. And there have been several Medicate expansion proposals that broadly match the scenario I outlined proposed by several Dems.