You are what you eat. You cannot outtrain a poor diet. I wouldn't have activity every day as the body needs time to repair itself. You break down the body during exercise; your time away from the gym/activity determines how well or poorly you repair and recover. As far as what to eat, I am a proponent of metabolic typing - eating the proper ratio of fats, carb, and protein for YOUR metabolism.
You will need to be in a small calorie deficit daily in order to lean out. Your resistance training should allow you keep the muscle you have and your activity/diet should foster a small calorie deficit. I am not a huge fan of your training split to be honest. I will let your trainer handle it though.
Your aerobic training should have your heart rate in the 70-80% of max heart rate in order to maximize fat calories burned. You can calculate this range by using this formula
(220-Age) x % Max heart rate (i.e. 70%) = # beats per minute for training zone
This will help identify your ideal heart rate training zone. You may also want to work in some short duration, high intensity anaerobic work (80-90%+ of max heart rate) to foster testosterone and HGH production as well as further improve cardiorespiratory efficiency.
As far as the shin splints go here is a protocol to help deal with them as well as some potential reasons why suffer from them -
weak anterior (front) of lower leg
poor movement mechanics/running form
improper footwear/arch support
weak posterior (back side of the body)
stretching - hips, IT band, ankle mobility, hamstrings, quads, hip flexors (psoas)
strengthen the anterior tibialis (front, lower leg) and the entire posterior chain (back of the body) - weak posterior = instability = compensation = pain
increase strength, stability, and flexibility at the hips to minimize compensation
improve core stabilization -- weak core = unstable pelvis = unstable hip, knee, ankle
assess posture and correct any areas of inflexibility or lack of mobility
continually seek imbalances and correct them