Regarding the external back up drive, I just did it's first back up. Do I have to plug and do back ups every day, even if im not doing any changes other than browsing the web and answering email? Also did that back up included my itunes library, which I suppose it did. Second, should I do a separate back up for my itunes library?
I don't know how mobile you are with your MBP, but I would suggest as long as the laptop is sitting somewhere plugged in and being used have the external HDD plugged in so TM can do it's thing. Or, if you are very mobile, plug it in at least twice a week.
Since TM backs up the entire internall HDD, yes, your music was backed up as well. In your situation I don't know that a seperate backup just for music is all that necessary. Some folks may disagree wtih me on that, but the decision is yours really. How secure do you feel with your present backup solutions? If you don't feel secure, then perhaps you might look into an additional backup solution, such as a true cloud backup like Backblaze (which I use) or Mozy. Where your precious digital data is concerned you can never be too redunant, in my opinion.