Crock pot lid askew

I suspect "warm" is meant to maintain temperature, rather than raise it. My crock pots are too ancient to have anything other than "high" and "low", so I can't assert any real authority. However, if you reach 145F within the first hour at the highest setting, then keep it at "warm", and test the temperature after about 30 minutes with an instant-read thermometer and it stays around 140-160F, you'll probably be fine. Personally, I'd test the temperature first by cooking water.

If the temperature stays above 140F at low, the worst risk you'll have is overcooking. Beans and vegetables like carrots and celery can overcook fairly easily in a crock pot, but higher collagen meats meant for stews tend to be fine when cooked for extended periods. Most crock pot recipes for stews and soups usually hold fine when at low for a full workday, although that's presuming a somewhat 70s-era soup aesthetic, which is probable for a crockpot recipe.

However, I would be inclined to attempt the recipe using the low setting rather than reducing it to warm, if you're not going to test the temperature first. If it turns out to be overcooked, you can always puree the ingredients with a blender...

I also doubt that switching to "warm" would be dramatically less likely to overcook the food than "low", unless it holds at a pretty stable 140F, and low ends up somewhere around 160F.

You don't need to add any water to the slow cooker whatsoever. Your recipe is somewhat similar to the one that I use to cook my lunches but the quantities seem larger than mine, much larger. I assume that you chop everything up into small piece, including the chicken. The slow cooker should not be more than 3/4 full, so reduce your amounts if the quantities are too big.

Chicken breast doesn't need more than three hours on the 'high' setting in order to cook (six hours on low); this cooking time leaves most of the vegetables crisp (courgettes and pumpkin soften, but bell peppers, carrots and onions retain their texture).

Running a kosher kitchen, I would not know about adding cheese to the food, but anyway I would recommend adding the cheese to the food prior to serving, not while it is being cooked.

If you wish to separate some of the vegetables, one technique which I have used successfully is to put these vegetables in a wire tray (I use the plastic punnets in which we buy fresh mushrooms): these vegetable are cooked like the rest but are kept separate.

If you do wish to add certain vegetables after you have already started cooking, then you are supposed to add 20 minutes to the cooking time (every time one opens the lid of the cooker, steam escapes and it apparently takes 20 minutes to obtain the same amount of steam).