Will a facelift help minimize the appearance of wrinkles on the cheeks? (photo)

The short answer is "yes." Skin laxity is well addressed with facelift surgery. You can undergo surgery without addressing the neck if you prefer.
Best of luck to you!

Yes , a facelift will tighten the skin which will improve the wrinkles but not eliminate them. Laser resurfacing done in combination with enhance the results. However some of the wrinkles are due to loss of skin elasticity and with facial expression and muscle contraction it is inevitable that some wrinkling will occur. There is no treatment that will enhance skin elasticity.