Contract Law是否有效合約?

I would say the ans a7day6night stated in Q1 is not correct
Since Peter, the offeror, has clearly stated the method for communication of acceptance, any other method of communication will not constitute a valid acceptance. This principle is illustrated in Manchester Dioceasan Council for Education v. Commercial and General Investments Ltd.
Therefore, postal rule is not an importance discussing element here.

Since advertisments are mostly invitation to treat(Partridge v. Crittenden)(*except unilateral offer")
The situation now is that there is still no contract between either Peter and Mary , and Peter and Ben.

You should look up your law textbook to answer the question. This answer will only guide you what you should really do.

This question raised the following area of contract law:
a.) advertisement (tends to be invitation to treat, unilateral and bilateral);
b.) There is no unlimited supplies of goods;
c.) offer needed to be communicated before accept;
d.) Postal Rule, specified method of communication;
e.) Counter-offer;

To begin, you probably better to express and explain briefly what area of this question has touch upon, then discuss the above, sitting case law, explain each and every situation that could arise, then discuss the situation in the question, at the end, provide a conclusion.

To your first question, since that Peter received the acceptance at the same time, Peter will needed to communicate to either Mary or Ben before their offer is accepted (Lord Denning in Entores Ltd v Miles Far East Corporation), at the end, it is Peter choice to who he accept.

Second question, the reply has nothing more than an acceptance, but since the communication of offeree and offeror has not yet been established, Mary expression is merely an acceptance that is waiting to be communicated.

Third question, Postal rule will needed to be discussed. You need also to care about Ben's specific method of acceptance to his counter-offer.

I don't see much that needed to be discuss on your Fourth question, however, most questioner wanted to see what is your view to the question, expressing your own opinion, backup with case law and the supporting authorities, would give high mark in your exam.

Fifth question, I will only name some, you should look it up in your textbook:-
Fisher v. Bell; Carlill v. Carbolic Smoke Ball Co.; Partridge v. Crittenden; Felthouse v. Bindley (for being bound you need to take action); Adam v. Lindsell; Gibson v. Manchester City Council; Hyde v. Wrench; Harris v. Nickerson

2012-01-04 13:49:11 補充：
My mistake, q1, Ben's Tue Counteroffer was rejected, there can't be contract, so Peter is not bound with Ben. The only communicated acceptance is Mary's.