Actually you are probably going to want to bump up your changes to twice weekly and get a test kit. Or at least have you water tested by a reliable pet store and ask for the numbers to know just where you are in the cycle. Your tank may already be cycled.
As for changing the filter, the activated carbon runs out in about a week. But if you change the cartridge every week, then your tank won't be able to hold a steady cycle because you are throwing away the good bacteria. Personally, I don't use activated carbon filters anymore because they are a moneypit. If you change the carbon often enough to keep it working properly then you end up dumping at least $100 a year on cartridges.