Does signing on aim on my phone costs money?

Usually, signing on to AIM counts as internet service, not texting service. It won't matter how many AIM messages you send, internet charges by the MB. You'll want to be sure you have adequate internet service for your phone (it charges per MB, so it adds up fast). Being signed in to AIM then replying by text uses two services, the charge for the internet usage, then the additional text charge.