(b) Yes. The assurance that B Bank has given to A is an example of a 'letter of comfort' - a written assurance to a creditor that a debtor will perform their obligation. Whether or not the letter of comfort is intended to be legally enforceable against the person giving the assurance depends on what can be inferred from the circumstances of the case, and exactly what is said in the letter.
If the statements in the letter are not promissory in nature, then no intention to be contractually bound will be inferred. In the present case, the statement does not contain a promise by B Bank to make good any loss if C fails to pay. There is therefore no evidence of an intention to be contractually bound by the letter of comfort.