You should really do some research. Your questions are really "beginner-type" and answers can easily be found by doing some research. I am not trying to put you down or discourage u from asking questions, but when you are starting a hobby it's helpful to know a little bit of background of what you are getting into.
Yes, you can grow VFT's indoors in a terrarium, although it is a poor choice because these plants require LOTS of bright sun in the growing season. So, growing outdoors is the best option. Make sure that your cities winter temperatures are close to the annual temperatures of those in the Carolina’s during the winter.
Also, make sure to read about winter dormancy.
Yes, peat moss is fine. Some people like me like to add perlite to enhance drainage. Also, make sure that the growing medium that you will use is non-fertilized!!!
I have never grown VFT's from seeds so I can't really help there, except that I know that it take up to a month before seeing any growth.
I have never grown or kept pitchers so I can't help there, sorry.
I really suggest going to terraforums and reading through the topics they have there on VFT's they are really helpful.
Good luck!!!