Can I lengthen and slim my fingers? (Photo)

Ms  J8e98n, your hand is beautiful. I would never recommend you do anything to those fingers. They look pristine (:  Ask any of our hand surgery patients who have undergone surgeries to help repair their tendons, bones and nerves what their life is like they will admit that stiffness, difficulty in grip and day to day hand use is very burdensome and psychologically draining . When we operate on the hand,  at best, we aim for near normal form and function, not forgetting that the more surgeries you undergo the more scars, adhesions, pain, risk of infection or bone not healing well or not healing at all. 

Whilst it is possible to extend bones (by 'externally fixing' them to cause 'distraction osteogenesis'), there are multiple major considerations of the risks involved. 
Importantly, such treatment occurs over a prolonged period, you shall have multiple scars which may be extensive (have you considered how you'd react to this?), and there shall be great inconvenience and compromise to your life.  
Above all, I very, very strongly doubt that you shall get enough length and change to meet 'your expectations'. Furthermore, I cannot name a single surgeon who shall be willing to fulfil your request given the nature of it (i.e. aesthetics/ lifestyle and 'not' disease or trauma).

You actually can lengthen fingers using the Ilizarov technique for legs.  However, there is a large risk of finger stiffness and other complications.  The trick will be finding someone who would be willing to perform the procedure, and there would be multiple small scars along each finger that was lengthened.  My personal opinion would be that it would not be worth the risk and I personally would not perform it.