As to proving anything, my understanding is that it is theoretically impossible to prove, but sometimes bugs in the implementation or various user mistakes mean that you can, in practice, sometimes get a good indication that something is hidden,
Although file-hosted TrueCrypt volumes (containers) do not contain any kind of "signature" either (until decrypted, they appear to consist solely of random data), they cannot provide this kind of plausible deniability, because there is practically no plausible explanation for the existence of a file containing solely random data. However, plausible deniability can still be achieved with a file-hosted TrueCrypt volume (container) by creating a hidden volume within it.
It's impossible to tell an encrypted volume header apart from random data. It's very much "try, and if you fail, you either have the wrong key or the volume doesn't exist".
Page: http://iq.org/~proff/rubberhose.org/
Description: http://iq.org/~proff/rubberhose.org/current/src/doc/maruguid...
As for the data loss, if you only enter the first password, it will let you overwrite the space where the hidden encrypted volume is stored yes. How else would it work? If it didn't let you do this, it would be obvious that a hidden container exists...