Myfitnesspal is very good for some things, and I recommend you make a habit of using it later in this process. However, its very bad at figuring out your targets and goals for you
I think the important thing is to get the quality of your food sorted first. A doughnut and a sweet potato might have the same amount of carbs and hit your macros in exactly the same way, but it doesn't take a genius to figure out which you should be eating. This applies even more so if you're used to eating sugary rubbish.
That's all very well, but as I've said above, macros don't show the whole picture so what exactly did you eat yesterday? As in, in real food, not numbers on paper.
I feel precisely the opposite. I feel that a lower carb plan on non-lifting days will steer you away from the breads and pastas and towards using lots of veg and some fruit as your main carb sources.
I would say that eating loads of carbs because of the tiny amounts of other nutrients in them doesn't make a lot of sense either. Especially when those nutrients could come from veg. I also find it hard to believe all those carbs came from fruit. That's about 8 apples, which would be getting on for a third of your total calories for the day.
I personally think heavy lifting should be an important part of your plan, and that the specific program probably isn't that important or something to focus on. However I certainly don't think it should be the only part of your plan, you should be trying to move pretty much as much as your body allows. I don't know your fitness levels so take some of my recommendations with a pinch of common sense, but things like walking a lot more, some of it with a weighted vest, a few sessions of bike intervals a week, swim a few miles, join a local team and play once a week, etc. etc. etc. Get your activity levels up. I lost about 5 stone (70lbs) by making a rule that every day I was going to do some form of exercise. During motivated periods, I'd often do 2 or 3.
Your attitude seems to be spot on, and will serve you very well. Just remember fat loss doesn't need brains or talent or skill, just hard work.
Can I recommend spending Saturday as a meal-pep day instead? I know looking for routines is fun and chopping veggies isn't but one or two days a week planning and buying the food you will need will make all the difference.
EDIT: Also, your gym sounds immense, I am very jealous.