some can't access your funds if you lose the password or id, but they have secret seed that would allow you to recover the wallet, and you may export the private keys, so you would not lose your funds
the answer depends on the service
agree. probably an online wallet provides a service to recover your wallet, but offline ones do not because you own the private keys. however, I ever read the policy of an online wallet that they cannot recover your wallet when you lose your identifier. so the key is identifier. if you still have it, I think you can get your coins back.