(2) The server gets sent your password every time you log in. You shouldn't rely on a server operator not knowing your password.
(3) You can tune how sensative the system is in response to changes in the fingerprint. Even if their in a failure to match that just means authentication will be extra strict.
(2) The server gets send the password via the default communication channel, the browser, TLS hopefully, not via e-mail, possibly into an inbox, that is third-party controlled (say some google mail inbox for example).
(3) That does not make it right. Did they even ask the users for their consent? Did they learn anything from GDPR or in general discussions about consent? Or are they just a higher being, allowed to decide for their users, what data about them they track?
Many things can be done using technology. The question is always: Should we do them? That is a question about ethics, not technological possibility. We already have far too many businesses not caring about ethics at all, we do not need any additional ones.
(2) That is how it usually works.
(3) You can collect the information for security purposes just fine under the GDPR.
Providing a better user experience while maintaining a similar amount of security is a net positive
(2) Are you missing the point? "That is how it usually works." -- So why then send a password to an e-mail inbox, like I said a location often controlled by third party and often one with no good record of respecting privacy, if you can completely avoid that?
(3) OK, seems like we did not learn about consent. Why don't you ask your users, whether they are OK with it first, instead of assuming and basing on what is legally possible? Is ethics something too far out of reach?
Lastly a word about what you call security: Your so called security is observed often enough to result in inaccessible accounts. "Extra strict" usually means something along the lines of "oh, now I am going to require your phone number, to send you a message on a second channel to make sure" or "solve these captchas for this untrustworthy third party provider and I will trust their word about you having solved it correctly" (again being tracked of course ...) or similar things. Again circumventing consent, because now it becomes an extortion, extracting more personal data, so that the user can access their account. Your so called security makes for a real shitty user experience and punishes the user for ever switchting their browser.
So what does your "extra strict" mode entail? How are you going to be "extra strict", without any extortion? Are you implementing your own captachas by any chance? Or something similar?