I don't have any money on my account right now, do you know if the charge will accumulate every month or something until I pay? I don't see the option to cancel anymore, it only says past due and I noticed that the service is no longer provided. 

It will not accumulate every month. It will kill the subscription and eliminate service until you resubscribe.

Correct; The subscription will just stop - no charges.

If there are any issues you need to have examine, please don't hesitate to contact Support.