Thanks for the details! "Normal start" is a step up in difficulty from the tutorial, which is easy difficulty. Difficulty is mostly reflected in how (dis)obedient slaves are when you acquire them, how easy it is to get positive outcomes in interactions that they don't refuse, and how expensive rental costs are.
Your games that ended due to health were because you lowered your strength into negatives by spending too much energy. Eating low-quality food (which is all you have in the slums) lowers health every day too (but won't directly kill you), so starting with a low health character like Johny means you need to find a way to build up strength, or else be extremely careful about how much energy you spend. Drugs (kamra, faerie pollen) can boost energy if you neglect your strength for too long. Faerie pollen is harmful, and kamra also if taken too often, but occasional doses of kamra won't hurt you.
You can build strength by eating at the tavern in the Serpentine district (at most once a day) or having sex at the brothel (limited by the slaver's excitement/libido and energy), or winning spars at the colosseum (equip an aketon to boost combat skill and use a weapon and you can beat the unarmed slaves right away, or lose fights repeatedly to develop basic combat skill the hard way), or personally training weaker slaves in athletics or combat (easier to do if your slaver is not weak himself), or having sex with slaves (if you visit the Slums after renting an apartment you'll get some help with this), among other methods...
Your game on normal mode, you gave her rules she wasn't obedient enough to follow (humility, maybe chores too). Rule-breaking lowers the slave's obedience so you were somewhat undermining your progress with this, but punishing her increases obedience, so the question is whether you were making progress or not, and that depends on the slave's stats compared to the slaver's and what methods of punishment you used.
I would guess you probably were making progress (she was becoming more obedient), but at the cost of her mood. Over time, with bad mood or too many punishments, a slave's despair increases, which can lead to escape, rebellion or suicide attempts. Escape can be prevented with a collar and brand. Rebellion can be prevented by having a stronger aura than the slave (high slaver stats + wearing noble regalia and/or artifacts + magic spell Magna Magnifika). Suicide can be prevented by an assistant tasked with supervising the slave. All of these undesirable situations also can be prevented by keeping the slave's mood in the range of Pessimistic or higher.
At a certain level of obedience (different for each interaction), the slave will stop refusing outright and instead the text will indicate that "she doesn't listen at all" or otherwise performed very poorly. The text also gives hints about how to improve her performance. Did you see that? If you're trying to get her to do something that she refuses outright, it's also not a bad idea to try something else. For more hints along these lines:
https://f95zone.to/posts/9401682/
It's ironic that for your easy difficulty attempts you didn't actually try to train a slave but instead jumped into combat, which is an entirely different set of mechanics and isn't designed to be
easy even on easy difficulty. Note however that starting a custom game on easy difficulty adds a cheat sub-menu to the options menu where you can make your slaver immortal in combat if you want.
If you don't want to do the tutorial, I suggest starting another easy custom game and getting a slave from the market or from the guild. The advantage of the tutorial is that you don't have to know your way around the city and you have a ready supply of clothes, high-quality food, access to plumbing, etc. It's a reduced set of concerns so you can focus on the training aspect. There's also a "debug info" button that shows you in detail how the slave's obedience is calculated and you can observe how it's affected by your actions. Something equivalent is available in the regular game by acquiring a certain artifact.
