You can choose any x as long as the coefficients are random. I don't quite see how randomizing x achieves anything, as you have to provide entire points (x, f(x)) as fragments, therefor x is public information. Maybe you were trying to say that the x values should be chosen at random, instead of say, as part of a sequence? I don't think that's relevant at all for SSS, since all operation are performed on a finite field.

The coefficients are 32bytes, therefor your backup would have 5 lines (1 header line + 4 * (16bytes of data + 2bytes of checksum) lines) per fragment. If the fragment only has 1 header and 2 data lines, it's using implicit [1,...,N] for x.

It's far worse than that. Look at how the coefficients are constructed, they're hashes of the previous coefficient. Whatever fragment the attacker gets access to, he will be able to compute all following coefficients just by hashing x once.