I'm not sure about the hydramatic question, but Packard used their own tranny called the Ultramatic. I don't know much about them but I don't think anything interchanges. Of course some models may have used hydras too, especially the later models when Packard was struggling to survive.
There was never much speed equipment made for Packards, and today it's a rare find. I saw one finned alloy head at swap meet, priced at $600 and it was about the size of a surfboard. I've seen dual and triple intakes but they were home-built specials. This was the problem with the "orphan" cars, never enough of them around to merit aftermarket speed parts. Especially Packards, which were high-end luxury models. Keep an eye on E-bay, but don't hold your breath.