I can't feel the tip of my fingers after surgery. Is this a result of the anesthesia?

Not Directly. This is not due to the anesthetic drugs, but is more likely due to positioning during the operation. Once you are asleep pressure can be placed on the nerves supplying our arms and legs. When we are awake we naturally turn and alter our position to keep this pressure minimized. The numbness should resolve fairly quickly. If it does not you should get in touch with your anesthesia provider.
Depends. I would need to know what your surgery was, what type of anesthesia you had and which fingers are effected.