Can Dysport cause numbness and twitching in your cheek and droopy eyelids? (Photos)

I'm sorry this has happened to you and want to reassure you that this will all resolve withing 3 months. The problem is not the fault of the Dysport but the injector. Proper dosing and placement of the Dysport is key to avoid droopy eyebrows. If too much Dysport is placed too low, the forehead will not be able to lift the brows anymore and that results in brow ptosis. Sometimes this can be remedied with placement of further Dysport in the brows or crows feet area. I can't appreciate the chin or numbness issues on these pictures but it all should resolve. I would pick another provider in the future.

I am sorry you are unhappy. 
Dysport and Botox are essentially the same product. Both temporarily paralyze muscles to soften wrinkles in the skin that is directly connected to those muscles. Luckily both are temporary, lasting only 3-6 months (3-4 months is more realistic).
Neither product should cause numbness as they do not affect sensory nerves.
I recommend you return to your physician to discuss your concerns.
Good luck.