Chicken – Will the food continue to cook on the warm setting

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.

It depends on what kind of settings your crock pot has. A low simmer on the stove is probably equivalent to something fairly low on your slow cooker, though. If all you have is warm, low, and high, you want low - in some cases it might be too hot, though. You're aiming for just short of boiling, so a setting that gets you a few bubbles now and then is good. More than that and you're cooking a bit vigorously, and on a "warm" setting you likely aren't heating it enough to cook properly and stay safe. If you have some kind of continuous settings, you can possibly adjust to get exactly where you want!