It is definitely a '64 after looking at some pictures. '63 had louvers at the back near the tail lights. '64 didn't.
1965 was the big square redesign.
Yes, and they a) cut 500 lb. out of the car and b) added a lot of sound insulation to quiet the car down. Remember how they advertised that the interior of a Galaxie 500/XL in motion at 50 mph was quieter than a Rolls?
They also changed the engine lineup. I mentioned the 289 -- that was not available until '65, my mistake. In 1964 the base engine was the four-year-old 260, delivered in the early 64-1/2 Mustangs. (My dad test-drove a 1960 Ford station wagon equipped with a 3-in-the-tree and a 260. Not impressed! 'Course, he was used to our '57 Country Sedan with its "Thunder Road" 312 Police Interceptor that generated 265 BHP at 6000 RPM when equipped with a Rochester 4V carb ....)