Workout Schedule Question

Basically, I thought I was doing everything properly, until I met with a personal trainer today who told me that I should NOT be going to the gym every day and should focus on a lot of stuff to increase strength. This is the schedule I have prepared, please tell me if it's good enough for intense workouts. I thought my 4 hour workouts were very intense, which they are, but I never thought the trainer would be able to completely exhaust me out in 30 minutes, which he managed to do with exercises that didn't even involve a lot of weight :O.

Please evaluate my schedule and tell me what changes need to be made to maximize quick muscle and strength growth. Keep in mind please that I have been working out for a long time (almost a year) so my muscles are used to intense workouts, so they NEVER get sore anymore, that is why I go to the gym everyday, AND I just started taking protein shakes to help me through. Thank you for your help

He also told me NOT to work biceps and triceps on the same day, or chest and back on the same day because they are action/reaction muscles, can someone confirm this for me, because I work all arm muscles when I workout my arms.

Monday:
30 Minutes Warm-Up Cardio
2 h 30 minutes CHEST WORKOUT
45 minutes AB WORKOUT
15 minutes cool down cardio

Tuesday:
30 minutes warm-up cardio
2 h 30 minutes ARM WORKOUT (BICEPS + TRICEPS + FOREARM) (+ 3 sets of Bench Press)
45 minutes AB WORKOUT
15 minutes cool down cardio

Wednesday:
30 minutes warm-up cardio
2 h 30 minutes BACK + SHOULDERS WORKOUT (+ 3 sets of Bench Press)
45 minutes AB WORKOUT
15 minutes cool down cardio

Thursday:
30 minutes warm-up cardio
2 h 30 minutes LEGS (mainly), SHOULDERS (minimum), + CHEST WORKOUT
45 minutes AB WORKOUT
15 minutes cool down cardio

Friday:
30 minutes warm-up cardio
2 h 30 minutes ARM WORKOUT (BICEPS + TRICEPS + FOREARM) (+ 3 sets of Bench Press)
45 minutes AB WORKOUT
15 minutes cool down cardio

That is basically my schedule. Can you guys please look it over, I know I am new to the community, but I plan to stick around, but I really need your help here. Please look it over and tell me if it's any good, and if any changes need to be made, let me know

Thank you for your help

P.S.

I need to know this - is it better when working on ONE body part a day to do as many different types of exercises possible for MAXIMUM benefit, or a select few exercises?

Which is better for your body, and will help me gain muscle mass and strength faster? Right now, when I workout on one body part (say CHEST), I do 3 sets of Bench Press, 3 Sets of Dumbbell Flyes on the incline, and 3 not on the incline bench + incline bench press 3 sets. On TOP of that, I do 3 sets of about 10 machines that the gym offers me.

Now I am confused after meeting with the personal trainer today, which is better for MAXIMUM BENEFIT (taking in mind my muscles can take intense workouts, and I take protein shake (just started)), the workouts I do with the many different exercises, or for example the type of exercises this site offers, 3-5 exercises for one body part a day.

Also keep in mind, that I am trying to gain muscle mass and strength in the next two months, so which is better?