I have done a similar weight lifting plan and did not change my eating habits and lost a whole lot of inches (went from a size 14 to a size 8 in six months) and lost a few lbs. In terms of calories, you can just add on the 200 cal for the protein shake when you are weight lifting to compensate for the workout. There can be a small calorie deficit (if my understanding is correct) but not a drastic one because your body will just "eat" the muscles that you are trying to build.
More muscle=higher metabolism. higher metabolism=easier weight loss.
For increasing weight, experimentation is allowed. Once you get used to it, you can tell if it's too easy for you to do the movements with the weight. But if you are unsure, add on a small increment (ex. 5lbs on a weight machine or 2lbs in dumbbells) and try the exercise performing the same proper form. It should be challenging, but not impossible. For the NROWL, they have it so you gradually decrease reps over time, which theoretically makes you increase weight. The less reps needed equals more weight you can perform. For example, I can press 50lbs in 15 reps in proper form, but I can do 70lbs in 6 reps in proper form.
I also feel for you about his plan, doing the same things over and over. Since I had the previous experience working with a personal trainer, I know how to scramble things up and make it personal to me, since not everyone is the same. I divided workout days into core muscle group days (leg day, back day, chest day, etc.) and it keeps things interesting. Also mixing up the cardio makes things interesting as well.
So yeah (TL;DR)
-Up calories to feed growing muscles (200cal protein shake)
-Muscle training increases metabolism, which promotes weight loss (mostly evident in inches rather than lbs)
-Experiment to increase weight, but keep proper form
-Feel free to deviate a little from the plan to keep things interesting for you