Bitcoin is never truly anonymous. If you buy BTC from someone/somewhere that needs ID, they know the address you buy the bitcoins to are owned by you. Blockchain.info makes no difference on that. If you don't taint all your addresses though, not everything can be tracked back to you. I don't think using a VPN will lock you out, but maybe trigger email 2FA but that is it. Not sure about the Tor thing, so it might be good to backup your private keys just in case.