A GSO Projection does remove the fermions from the Type 0 string theories. In fact the two theories (0A, 0B) are exactly differentiated by their chirality, which is decided by the GSO projection.
However, the Type 0 string does not have spacetime supersymmetry (only worldsheet supersymmetry), and doesn't contain fermions in its spectrum.
As for dualities, there is a T-duality between the 0A and 0B strings,  (.ps.gz file, direct download),  (.pdf file, direct download) , .
Answering your last question, there is some interest in two-dimensional type 0 strings, and it's also used as a toy model to study closed string tachyon condensation among other properties.