(a) Yes, that's right. Normally, to be effective, an acceptance must actually be communicated to the person making the offer. A wanted a reply within three days and did not receive B's letter within that time. But acceptance by post is an exceptional case. Acceptance by post takes effect when the letter is posted, not when it is received. So B validly accepted A's offer, even though A did not know about it.
Acceptance by post is as appropriate as any other way of communicating acceptance, unless the person making the offer indicates that acceptance by post is not acceptable. In fact it is always open to an offeror to state exactly how acceptance must be made.