Would a plant or animal carry out cellular respiration in its cells?
They both do!
It's a pretty common misconception that only animal cells undergo cellular respiration, for a while I even thought that until my teacher told me otherwise.
Basically, an animal cell, say a human muscle cell, takes the glucose that was provided though food, and uses it for cellular respiration (C6H12O6 + 6O2 ---> 6H20 + 6CO2 + ATP (heat)).
For plants, photosynthesis is simply autotrophically making that G3P molecule which can then be turned into organic compounds (like glucose) for cellular respiration to make ATP.