Okay, trying this again.
re: your first question (which apparently I can't quote) - I'm not sure what the difference is between dye-based and pigment-based inks. I did a quick search and found generic information that says pigment-based inks tend to be more vivid and permanent, but I didn't find anything that addressed how these inks work on fabrics. You might contact the manufacturer of Bubble Jet Set to see what they say, just to be safe.
re: your second question - I meant if you're using Bubble Jet Set. I have no personal experience with simply printing on untreated fabrics, although I have a couple of friends who have tried it and tell me their items have faded.