Mutual Authentication with EAP-MD5 

Dear all, 

I hope it is right place to ask this question. 
In these days, I am learning a protocol verification tool and trying to verify 
EAP methods. 

I want to see if the tool can find known attacks that can be launched to these 
protocols. 

And started with basic one - EAP-MD5.  

The [rfc1994 CHAP 1996] states CHAP protocol is only one-way authentication. 
But by negotiating CHAP in both directions the same secret set may easily be 
used for mutual authentication.

In [rfc3748 EAP 2004] it is said that the sequence of Requests and Responses 
continues as long as needed.
The Request packet is sent by the authenticator to the peer. 

My questions are: 
1) Is it possible to mutually authenticate Peer and Server using EAP-MD5 ?
2) If it is possible then how will messages exchange ? 
3) is it possible that peer also can send request (Or may the Peer can send a 
challenge in the Respond packet) ? 

4) Can it be like following : 

P <-- S :    Request_Id
P --> S :    Respond_Id.User_Id

P <-- S :    Server_Challenge, Server_Id
P --> S :    Hash(User_Id.Secret.Server_Challenge), User_Challenge
P <-- S :     Hash(Server_Id.Secret.User_Challenge), EAP_Success                
 
        % or EAP_Failure 


where
P            : Peer
S            : Server
Secret         : Password (symmetric key) 
Hash         : One-way hash function 


I'm very not sure, 
Please correct me 

Your help would be greatly appreciated

Thank you very much 


P.S.  I think I explained what my problem is. My English is not good. 
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