Some business communications quickly take on the flavor of a personal chat - in which case, first names are appropriate. Others remain on a formal level - in which case, retain the formal address. Consider age and rank, too, if it can be discerned from the correspondence. Outside North America, people in a position of authority and people of mature years expect a certain deference from their juniors. HERE for International Addresses and Salutations.
Correspondents frequently try hard to be brief.
This is desirable, but business messages will usually be longer than personal notes. It is important, also, to communicate - don't kill understanding with brevity. When replying, you will often be replying to only part of the received message. Maintain the thread, by all means, but save space by not returning the whole message, only the part to which you are replying. These are fine for personal notes but are quite inappropriate for business use.