The PVC pipe thing is indeed an isolator, and these are generally a good thing to have. They can help with R.F. ground-loop problems. You may not need it, but I can't think of a good reason to remove it (unless it's faulty). There's not much that can go bad inside the isolator -- it's essentially a bunch of ferrite toroid cores with the coax running through the middle.
As for adding ferrites to the power and control leads, it can't hurt. Here's a link to a presentation I recently gave about SSB and satphones, including a section on EMI: SHTP Communications 2012
. About halfway through it I give some details on appropriate ferrites and their application. The particular ferrite I mention is optimized for SSB frequencies
I'm going to let someone else advise you on the power connection points. There are many ways to get this right. The SSB itself may benefit from a direct battery
connection, but the tuner power connection is less critical, especially if you use ferrites.