1. I think a pitcher filter is alright because I use mine on all of my CPs which include neps and vtfs.

2. You should try to have the plant in a big enough pot so that it will have all the room to grow. I just don't recommend repotting despite what anyone says because plants could have transplant shock and they will have to keep adapting to their current environment. Try not to hassle with them too mcuh! But yes, if your plant's roots are filling up the pot you should repot, but get a really big one so you don't have to repot anymore.

1. So long as the pitcher filter you use removes mineral contaminates like calcium, copper, magnesium, and salt, and does not add any salts for taste, it should be fine.

2. Just to add, Nepenthes are tolerant of repotting.... If you used too big a pot you would need to use much more water and soil than usual. In addition, you would need to repot every year to keep the peat from souring... peat moss only lasts so long before breaking down and creating a potentially infectious, and smelly, environment. At most, you might get away with repotting every two years. Use a pot that is a couple inches larger than its present one and use a well draining mix like one part peat to two parts perlite or one part peat, one part coconut husk, and one part orchid bark.