You seem to have intuited the crux of the issue here, which is that the personal training industry is besieged by charlatanry, and you are a victim. It’s not like going to the dentist, where there are reasonable minimum standards everyone has to meet. A weekend fly-by-night cert is enough for someone to legitimately title himself a ‘trainer.’ The “zeroed out” thing doesn’t make sense to you because it has no basis in science or practice or anything. A professional should be able to explain things clearly to you so that you understand your plan. A quick survey of the fitness and athletic landscape should make it plain that this is not necessarily a pursuit that selects for intellectual ability - there is nothing complicated about physical change, it is just hard, grinding work, and you have to sustain it over a long period.
Your plan looks dreadful to me. I understand people have different training philosophies, but unless you are morbidly obese or recovering from a coma, that does not look to me like something that is going to be impactful. Moreover, even if balance is something you want to improve (for a sport or whatever reason,) research is pretty clear at this point that it is not a highly trainable quality, especially in adulthood, and to the extent it is, it should be trained as specifically as possible (i.e., if you’re a figure skater, balance/proprioception training should happen in skates, on ice). Not seeing the value of standing on one leg for 30 seconds, or whatever “one foot balance” means.
In terms of your calorie issue, standard practice to lose fat would be to start 250-500 cals/day below your maintenance calorie level and adjust from there as needed. The cals this person has you eating are actually fairly reasonable, maybe a shade low, but like you said, you’ve been undereating dramatically so your metabolic rate has probably compensated a great deal. Even a broken clock is right twice a day.
This is the information age…I get that people are busy but you sound intelligent. I’d say 30 minutes to an hour of research online would be enough for you to put together a far better plan for yourself than what you’ve paid this man for. The T Nation archives alone have everything you’d ever need.