First case
The first, The key issue is Red ChIlli asked ABC for information, and they satisfied with each other, but the Red Chilli did not buy goods from ABC, they bought form other company.
The relevant principle is “a mere supply of information is not an offer”. This principle tells us if purchase only ask some information about the goods which purchase is interested in, there is not an offer between them. ABC put the advertisement on its website and stated that purchase orders could be made by fax, letter or online communication. The fact is the Red Chilli sent e-mails to them, that was asking question and trying to get more details about the goods, but the ABC treated it as an offer. Thus, there is no binding contract beeen

Second case
First, the key of the second issue is ABC did not agreed the conditional offer. And made a new offer. However Martha cancelled it.
The relevant principle of this case is the acceptance of counter offer. A mere request of information would not amount to a counter-offer. And also acceptance is a final and unconditional expression of assent to the terms of an offer, once given it shall, become a binding contract.
When Martha fax to ABC, she said” order…”, and made a conditional offer. After nine hours, ABC replied meat reject the conditional offer. Tomorrow, ABC sent another e-mail for a new offer. After Martha read it. Once she put a letter in the mail box for cancelled, it was valid. Thus, there is no contract between ABC and Martha.