Necessary To Cut Upper Lip Muscle

Although it is hard to comment without seeing your pictures, cutting the depressor nasi muscle is not always necessary to lift and stabilize the tip of the nose

Yes, in droopy noses that droop even more when smiling, cutting the depressor septi muscles is necessary to acheve proper tip rotation and positioning.

Cutting the upper lip muscles is not a routine part of rhinoplasty. I do it when people complain hat there tip drops when smiling. This procedure must be acompanied by a good tip support procedure

Cutting the muscle does prevent the tip to rotate downward with facial animation like smiling.  This is a big issue for some patients who tell me they don't like the way they look in photographs or profile pictures.  Cutting the muscle is a technique I discuss with patients pre operatively, but I give them a choice as to whether it will be done.  There are few draw backs or potential risks to the procedure except for post op swelling.  

The depressor nasi muscle is cut  to minimize the inferior rotation of the tip with smiling or facial animation. There is little risk with this procedure. It is not necessary but discuss this alternative with your surgeon before the operation. 

 No, it's not necessary, nor a set part of a Rhinoplasty to cut or even to dissect the upper lip muscles unless part of the Rhinoplasty plan is to place cartilage or some other graft material to fill in a retracted columella.  Similarly, when the upper lip is dissected in that manner...it should not decrease the tip support.  Dissecting in this space can however, create additional space for batton and strut grafts to fall into if they are not secured with tissue glue or permanent sutures (it's always a good idea IMHO to secure all grafts).