Mozilla sends verification code to my email, but my email is so slow that by the time this code arrives it already expired. Can verification be done throughw a phone message or how can I increase the verification time to wait until I receive the code?

Sign in codes can not be sent to your phone via sms, and they do not allow you to extend the code expiration time. One thing you could try is logging in to your email via a browser instead of the email app which could speed up the time it takes for you to get the email. Another solution is to manually copy the profile on your old computer putting it on a usb stick and the opening it on your new computer.