Some corrections and clarifications:
1. A critical observation in the discovery of transduction was that the ability to carry out recombination in the presence of the filter was DNase insensitive (which distinguishes it from transformation) - which meant that it was not naked DNA that was responsible, but DNA that was somehow protected from the environment (in this case, packaged inside a phage particle).
2. In generalized transduction, recombinants are generated via homologous recombination between the transducing DNA and the bacterial chromosome and the resulting bacteria are not partially diploid, except transiently.  Specialized transduction, on the other hand, generally results in bacteria that are partially diploid for the specific region incorporated into the transducing phage's DNA
3. A specialized lambda transducing phage will carry genes from the gal region OR from the bio region, but not both. The same phage particle cannot carry genes from both sides of the prophage integration site.
4. Only temperate phages generate specialized transducing particles, since they are formed by aberrant excision of the prophage.
5. The Hershey/Chase experiment had nothing to do with transduction. It was examining the fate of the phage genome (32P labeled) and the phage particle (35S labeled) following the initiation of lytic infection.  To the best of my knowledge, T2 is not a transducing phage.