Well, one can have arbitrarily many Bitcoin wallets. I have dozens in current use. Each one is associated with an identity, at least an email address. Most of them only connect through Tor, so there's no IP address association.
But yes, if you don't compartmentalize like that, everything is linked.
You can have as many wallets as you like, but the problem is the same for all of them: getting coins into them. Transferring between wallets would obviously link them. You would have to go through a (different) convoluted way of obtaining the coins for each wallet.
Not at all. I work anonymously for Bitcoin. Under a few identities, each with its own set of wallets. And I transfer among identities using mixers. I generally mix at least twice, using throwaway intermediary identities. And each identity has its own Whonix instance.
But yes, if you don't compartmentalize like that, everything is linked.