Because ITF lacks a checksum, looking for it is quite prone to false positives. So, yes only certain lengths are accepted and the shortest is 6. You can override this. However, I'd suggest that ITF is far from the best choice for this.
I don't believe there is a minimum length for Code 128. It will reject a 0-length barcode (i.e. only guard symbols). You'd have to provide an example of the 'limit' to look into it more.