If you need an answer to the question Will minibb allow me to incorporate a subscription system like you described, then the answer is YES. However if you meant if miniBB has all that features by default, the answer is No.
You need to program additional features on your own, or you have a chance to hire our team :-) The implementation is the following:
1) Under users database table, there should be a field indicating their paid status. It depends on you how you implement the payment system. In most cases, it is enough that user field just has a flag 1 or 0 indicating is s/he a paid member or not.
2) Upon that field flag, only paid users are allowed to post - else all forums will be read only for them. It could be a build dynamically code in miniBB.
3) Upon user reply, you should check if the user is the author of the topic. It's also quite possible implementing some little custom code.