Those are quite a few questions...
First of all, I personally don't consider a sculpt done until I have cut it up + repaired it (made it ready for casting). This makes it easier to accept cutting your sculpts up after finishing the scupting part. I can remember pretty well how I struggled with myself before cutting my first mini up. This helps though.
As for how to cut your sculpts, it depends on what type of putty you have used and what parts you have to cut. It can be done with a sharp knife in green stuff or pro create or with a fine jewelers saw if the material in that particular spot is thicker. If you made a sculpt out of polyclay, most of the time you will use a saw to prevent cracking of the clay. Just use it steady and without pressure, let it cut through the material without forcing it and you should end up with a rather clean and nice cut. A good saw will also cut through the wire without problems. After cutting with a saw, there is always a certain loss of material of course, you can repair that by using putty again and while you are at it you can make little pegs to insert that part into the main sculpt.
As for nescessary cuts, that really depends on your caster, I have seen people cast things in one piece, that would be impossible for other services. A good rule though is to asume that you will use standard casting methods, as those molds tend to hold for longer and you don't know how good the caster is if you are working for a client. So just go with that and cut your models accordingly. A model has to be cut in places it creates undercuts and would "hook" itself into the mold. If you look at your mini from the top, everything that is not alined in one line and is pointing elsewhere( as in into the mold) will have to be most likely cut. This is a pretty bad example though and a picture of your particular miniature would help a lot.
As for cutting by the casting service, there are a few that actually do cut your minis up. Should your casting service offer such a deal, then it is up to you to decide if you prefer to cut it up yourself, a thing you will have to learn for the future anyway or have a total stranger fondle with your work ;) . I sure prefer to do it myself.
Once you have done it two or three times and have the mental approach of not being done with the sculpt until it is cut and casting ready it will become a routine. I know it is scary but... well you sculpted that figure, so you can fix it too.