For the heel-strike, the short answer is that neither one is inherently more or less healthy. The natural tendency among walkers is to heel-strike when walking along a smooth surface and to use toward the toe when walking along elevated or uneven surfaces.
The next time you go for a walk outside, do it barefoot and pay close attention to your feet. In my personal experience, heel-toe is the gait I use when walking steadily on a smooth, hard surface such as a clear asphalt road. It’s my “travelling” walking gait. But, when the surface gets irregular or when there is debris on the ground, I tend to shift to a modified forefoot walk. Why? Because bringing the bare heel down on a rock or stick hurts, so we adapt our gait on the fly to protect ourselves.
Your friends may be confusing the situation with barefoot running where it's pretty well-established that the foot acts as a shock-absorber when running forefoot-first while heel-striking results in a jarring impact before the foot rolls forward. Compare to walking where, instead of briefly being airborne with both feet off of the ground, you always have at least one foot on the ground.
As for turnout, a little outward turnout is the standard due to how our piriform muscles work (side note, both of those links discuss turnout as bad, but they also have some good information). From a physiology standpoint, extreme turnout tends to be an issue for two reasons. First, many people, particularly some dancers who have learned incorrect or self-taught, turn out using their knees as well as their hips. The hips are built to swivel (ball joint). The knees are not (hinge joint). Secondly, if you have extreme turnout, it's more difficult for your feet to cushion impact whether your're walking with your heel or your toe. It's simple geometry in that either your strides will be either pushing out out in lateral directions or you have a smaller length over which they will travel (they'll also not be moving along the length of the bones in your feet, which means you're inducing lateral forces along the bones, which increases the risk of them fracturing).
As to why a little bit of turnout is natural, take a look at this image of the bones of the foot:
Note how the metatarsus (the bone that leads into the big toe) is thicker and natural goes forward with a slight turnout. The means that, when walking or running with that slightly turnout, a majority of the force is being carried along the sturdiest bone in the foot. Doesn't that seem like it makes more sense than turning your foot in and and applying the force along your little toe?
