2. Ledger should be resistant to changes. Ultimate goal = immutable ledger
Running a privately owned blockchain is the way to go.
Private blockchains and immutability are exclusive, you can't have both. Ethereum's DAO debacle is a prime example of what happens to immutability when certain parties have too much power within an ecosystem.
I don't think so. If the blockchain can fail (meaning if an invalid block generated. It will die for those who consider it invalid). And it requires a single entity to control the chain. It's obviously centralized. But some applications don't require it to be open and public. This doesn't mean it should be permission based.
Immutability can help multiple users make sure either blockchain will fail or confirmation goes through. Still the main chain (bitcoin) can re-org and change the history of private chain.
Edit:
By this i meant. "This doesn't mean it should be permission based." => Still that blockchain can use bitcoin's code as Its base.
By private blockchain i mean, The ownership is private. It doesn't prevent the blockchain to get validated and used by other users.