1. Yay for live plants!
2. More, more, more! I jest. I just like live plants. :p
3. Running it for a week won't actually do anything. You need to add a source of ammonia, and when you do that it will take the BB much longer than one week to grow - typically about 6 weeks. I suggest reading the Cycling sticky. :)
4. Don't. Change the activated carbon, if you have any, according to the instructions, but don't change any other media. You can rinse it occasionally in dirty tank water, but that's where most of your BB lives, so every time you change it, you'll be destroying the BB and therefore your cycle.
5. Lucky little betta. ;)