First make sure you remove the old SSH public key from any of your accounts. Once you have Kryptonite installed on your new phone, add the new public key to the accounts you were using SSH with before.
Sounds like you ultimately need a backup method for logging into your server -- probably a second, non-Kryptonite key (or another admin user). Is that correct?
That is correct. We will also soon release a way to copy a key from one device to another by scanning a QR code.