I think you should take food first. The idea being that no food + demand for nutrients (exercise) tells your metabolism that resources are scarce. This makes your metabolism burn protein from your body (muscles) instead of fat from your body or proteins from your food, so if you are trying to gain energy or lose weight, eating first will be better at kick starting your metabolism.
There is no clear consensus. The few studies done suggest the opposite of what you are saying - that the glycogen depleted state your body is in when you wake up leads to burning fat before muscle. That said, most physiologists suggest you should eat something before working out. THAT said, most bodybuilders suggest doing "fasted AM cardio." I tend to go with the bodybuilders' advice as they are the ones actually putting their ideas into practice and figuring out what works and what doesn't.
And most busy people's morning breakfasts are not significantly portioned enough to risk indigestion against a workout that is probably about 5 minutes at the max (1.5 min. for rest time plus .5 min. for timing wrong plus 3 min. for doing LOTS of push-ups, theoretically). That changes if you throw in the core routine.
Most of us are just eating a bowl of cold cereal or having some toast. Not a full English breakfast.
you should always eat protein after workout.if you need to eat before as well depends on the amount of training.if you just do a couple of 30 sec series of pushups eating after should be sufficient.if you fail to eat after you will fail to gain strength
exercise is a great source of energy and i've found it also decreases appetite. I didn't feel the benefits until after a few weeks of a regular exercise schedule; during the initial ramp up the changes in energy and appetite were inverted.
