@jesusloverr You are right about the hazards of HS walking for good form. Dropping your weight ahead, arching the back, flopping the legs and catching the falls with steps can certainly instill bad habits. However, (correct) HS walking is much easier than standing still and if done well, it can certainly help teach you how to shift your center of mass.
This goes (again) a bit into the speculative realm, but (and all previous disclaimers about my limited expertise apply) Ive never felt that all practice has to be perfect all the time. It’s really important to focus on technique, but most of us are not professional gymnasts and simply want to be fit, have fun and be injury free. Quality training can certainly include a few attempts at handstand walking, or trying to hold a freestanding handstand as long as possible even if your form deteriorates halfway.
About head balancing: yeah its like you describe, although you can also use your nose or your chin to balance on. You best start off with a tall object, like a broomstick, because that’s easier (falls slower). Place on head, watch the top of it and move your head slightly towards where it falls to correct its balance. You’ve probably tried it on your hand as a kid. Cannot emphasize enough how my experience is anekdotal, but after balancing an object on my head, handstands feel much less multidimensional because your body only tends to fall back and forth (as opposed to all possible directions with an object on my head). Probably dont take it too seriously, but for a sore, quarantined rest day perhaps