I am designing an online portal website which would basically have the following functionality:
I am familiar with Joomla, WordPress, Prestashop, Magento and Yii, but I still do not have an idea of how to have a super admin for the complete website and an individual admin for each user account.
Any ideas on how this could be accomplished?
This is a custom job, there will be no one framework to accomplish your goals.
You should understand that frameworks are only a base layer of code that has been tested and proven secure. It's then up to you to use the framework's APIs properly to build an efficient web application.
You're best bet would be to pick one of the mainstream php frameworks:
Research each of the frameworks (this is not exhaustive) and choose the one that matches your needs and skill level.