In case of Mr A and Mr Mr C:
There is no contract; this is an invitation to treat. And on another hand Mr. C made verbal agreement not to sell the book to anyone else until Mr. A phones him back in three days with a new offer, this is a new contract, but it does not exist yet.
In the case of Mr A and Mr C, Mr A can claim that these was an agreement, and intention because it was a commercial arrangement, he also claim he providing consideration by offering to call back with a new offer.
Mr C can defend himself by saying that Mr A argue's was not variable considerable.

In the case of Mr D and Mr C:
However, next morning when Mr C took deposit from Mr D to hold the book for him till his 18 birthday, that mean he is bound an agreement between him and Mr D, but in meanwhile Mr C breach his a verbal agreement not to sell the book to anyone else until Mr A phone back in three days with new offer, breach his a verbal agreement by making another or new agreement with Mr D next morning, However, there is a contract between Mr D and Mr C but still is avoidable contract, the law apply its validity factors in contract one of the following factors a capacity of Mr D under age 18, that contract can terminate any time before his 18 birthday. The law apply the contract is a valid until it is avoidable.

Where is there a contract? how does the law apply? For a distinction grade you should make a supported case for who owns the book.
In case of Mr A and Mr A: so there is an agreement, and consideration between Mr A and Mr E, before Mr A phones Mr C to say that he will meet his original price of £1,050. and Mr A found out that Mr C sold the book, meanwhile, the agreement between Mr A and Mr E will be there is no agreement between Mr A and Mr E because Mr A couldn't give or providing consideration.
And this is an advertisement for everyone invitation to treat Mr C can sell