Making content available to a user after certain amount of time I  want to restrict content access to subscribers over a period of time. Each user should be allowed to access the content in a sequential manner. So, after one week of membership, users would be able to access "Week 1" material; after 2 weeks users could access "Week 2" material.
Membership would just be a particular role.

Something similar has been done in Drupal 6, using PHP as reported in Release Content to Subscribers in a Sequence.

I am wondering if this is possible just using modules, like Rules and Rules scheduler.
I yes I think this is possible using Rules and Rules Scheduler

Unpublishing Content

You should check out this tutorial  (its also for Drupal 6)

Publish content exactly 24 hours after it was created

What you have to pay attention to is just do the opposite. So in the action you say Unpublish. And then of course you pick the dates. 

Hope it helps