In the question, 'Those books belong to Rohan's brother, (question tag)?' Can we use 'aren't they' in this instead of 'don't they' as 'belong' here is not an action verb that's why I think that we can't use any form of 'do' here. Am I right?
You must use 'don't they?' if the tag relates to the verb 'belong'. The fact that 'belong' is a state verb, not an action verb, does not change this. 'Belong' is neither an auxiliary verb nor a modal verb, and thus the tag requires use of the verb 'do'.