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No, you can just change the password you receive and test several versions against the hash. So you stored your password with a lower first character in 2011 and now you enter it with a captilized first character. They can just hash it like you sent it to them but on top they can also first lowercase it and then hash it and that will then match the hash from the password you used when signing up.

Not necessarily, it could simply be checking both versions of the password against the hash

You just store multiple hashes, and don't support it retroactively

You don't even need to store multiple hashes, just check both versions of the submitted password against the one stored hash

No, they most definitely just transform the text to all the acceptable versions, do the encryption and compare it with the encrypted stored one.

Not at all, you just compute hashes for all of the acceptable forms of the password up front and store those hashes.