Various questions on encrypted partitions

["Jordi Gutiérrez Hermoso" <jordigh@gmail.com>]

So when I installed Debian, I told d-i to wipe the hard disk and
encrypt my lappy's hard drive. My tinfoil-hatted heart loves it.
They'll never take me or my data alive.

I am curious, though, as to the exact nature of the encryption. I'd
rtfm, but I don't know where to begin. I understand the encryption is
AES-256, supposedly good enough to keep spooks at bay, but how exactly
does it work? I chose a ridiculous 25-character random printable ASCII
password that I have committed to my cerebellum and muscle memory,
because I thought that AES-256 actually uses my password to encrypt
the hard drive. Is this true?

I also see that it uses something called LUKS, and I understand that
LUKS is the way to change my encryption password. How does that work,
exactly, at the mathematical level? If I change the encryption
password, does the hard drive get reencrypted a different way, or
what?

My last question is about potential data loss. Is an encrypted hard
drive more vulnerable to data loss than an unencrypted one? Suppose I
have a hardware failure or something. Will the encryption make it
harder to recover my data than if I weren't using encryption? That is,
if a few bytes are off, can AES-256 still decrypt gracefully?

Thanks,
- Jordi G. H.