it is possible, but generally hard to do by accident
like your stomach will hurt and you'll feel sick, long before you get to an amount nearing water toxicity
if you keep going beyond that then there's risks (mainly of hurting your stomach or throwing up, but possibly water toxicity too)

it goes along with not forming habits easily
like people will say "oh you don't have to think about brushing your teeth, you just do it" but for me (and lots of people with this kind of executive dysfunction) it's not like that, it's basically always a conscious decision and never becomes automatic

executive dysfunction can present like that, like that can be a symptom of severe depression, but when it's been that way your whole life and that's just your baseline, it's more likely to be related to ADHD or similar
so not necessarily super worrying, just a possible indication of some issue

congratulations!! 🎉🎉🎉

to me all that really stands out is that it seems unclear whether it's a kink thing or a communication method, it sounds like it's both? but in my head those feel like separate things
I think it's one of those things that depends on the individuals involved, what dynamic and agreement they have, etc

like I would sometimes show diary entries to people I was close to to better explain how I was feeling, because I could express it fine writing it to myself but couldn't express it as well in person
so that part makes sense to me, or like I could see how someone could be okay with it

and like mandating unlimited access to someone's journals would be a red flag *if* the person had a problem with it
but if they've both agreed that it's easier to communicate certain things via writing them down privately first then sharing them afterwards, I don't think that's an issue

like to me the main thing that stands out as weird is "this is how he's chosen to track your mental health and communicate", like if the sub wanted to communicate in a different way instead would that be acceptable, or is reading the journals the *only* communication?

I think it depends on how it was set up and agreed to, like say if someone agreed to the journaling requirement but then over time the punishments changed to be more intense, without discussing it first, that would be wrong
or if the part about reading it wasn't part of the original agreement

is it also counting your bmr or is it meant to be just calories burned like on top of bmr?
I think 1200 calories for two hours sounds kinda high if it's meant to be not counting bmr, but I have heard things like swimming or stair stepping can be about that much, so it can be possible

I think if you just sign your name in joined or cursive writing and do it often enough, then it'll form into a signature over time

personally I don't do a "signature", I just write my name normally. nobody's ever complained about it or anything.
so you can just write your name, or write it in cursive. I think generally the fancy signatures people get come from writing their name in cursive really fast so it all blends together