Sounds like your trainer is of a CW mindset.
Breakfast is not necessary. It does not jump start your metabolism. In fact, the old "breakfast is the most important meal of the day," thing came from a study that Kellogg did on seven and eight year olds so that Kellogg could market cereal. It's BS pure and simple for adults, and there are some studies that show you burn more calories working out on an "empty" stomach.
Calorie restriction and/or burning more calories than you usually do is the only way I can lose weight. With a qualifier. I have been over 200 pounds twice in my life. At that weight, I can lose about 20 lbs just changing macros. After that the calories are key. Other people's bodies are different, so I only speak for me.
1500 calories is fine. You'll lose a little faster on 1200, but the difference isn't too significant. If you can stick to 1500, but 1200 derails you to the occasional binge, then 1500 is better.
You're 35. You can probably handle six days a week of working out. But do know that it's not necessarily the most efficient way to go. Building muscle/lean body mass requires not only work, but rest. Short term okay, but in the long run (jmo) six days a week will lead to injury/fatigue/burn out.
If you eat a lot of animals (I include eggs as animal product), you normally won't have to add fat to your eating. Adding oils/fats to plants often facilitates the uptake of their nutrients, but animals come with their own fat.
Last note. What you're doing is stressful. Not all stress is bad, but stress is stress. Get a good amount of sleep and relaxation. And of course, good luck!
"Right is right, even if no one is doing it; wrong is wrong, even if everyone is doing it." - St. Augustine