Why is this page blank?
Where can I get a list of reliable peers and look at what fees they charge?
It is a list of nodes that blockchain.info considers to be well-reachable.
It's nothing authoritative - anyone can run a node, and there is no such concept as a 'hub node' on the network.
As to why it is blank: ask blockchain.info.
I think you will not be able to answer your first question without some history of being connected to the Bitcoin Network.
Just to explain, when you run a bitcoin node, it compiles a database of other nodes that it is connected with, so that when it attempts to communicate on the network, it already has a list of known IP addresses.
However, in any P2P network, other nodes come an go, some may not even obtain the same IP address when they return. In order to overcome this problem each node can share it's knowledge of other peers to any requesting node.
The point I want to make is that not all nodes are aware of all other nodes, and at any one time a node may just disappear from the network, only to re-appear with another IP address.
Reliable nodes are ones that I would have thought, tend not to disappear, and tend not to change IP addresses, and therefore your own Bitcoin node will be able to tell you what these nodes are (if it has knowledge of them), but only after having been itself connected for a considerable amount of time.
For the second question... this never happens. Peers do not charge fees - if they did nobody would connect to them.