Lot of stuff to address at once. I'll take a swing at some of them.
Your feet should point whichever way they point, what's important is that your knees point straight ahead. Knees are hinges and don't handle twisting forces gracefully. Depending on the amount of twist in your lower leg bones, your feet should point anywhere from slightly inward to somewhat outward.
Yes, the knee is only slightly bent, just in case. It actually straightens under load which puts more force on the hip during mid stance than walking with a locked leg, which refutes the bone density argument(which I'm not buying without some data - it sounds like a real stretch). Your knee not being locked doesn't mean that it flexes. Unless you step into an unseen hole, in which case it does, saving your ass in the process.
The video. Erm. Um. I had a real problem when she said to power your uphill walk by using your calves. Yikes. If you actually do that, you're going to be crippled with cramps in short order. The glutes power uphill walking through hip extension much as they power running. The gastrocs(the calf muscle pulling on the heel) are biarticular muscles that don't lengthen or shorten much during a stride cycle. All they do is transfer power from the glutes to the feet. Well, from the femur to the talus. The glutes drive the femur. She is right that most people use their quads too much. But the answer is to use the glutes instead. In addition, really.
Going downhill. Yes, your pelvis rocks. And your knees are bent. And your quads take a beating. I don't understand why she doesn't talk about the pelvis rocking during uphill walking. The gluteus medius on your stance side raises the opposite side of your pelvis as you extend your hip. That happens on flat ground, too. Seriously, everything moves together, your spine, your hips, your legs, your arms. Heck, even your neck and head. Focusing on one or two body parts and trying to force them into a specific pattern can lead to more problems elsewhere ... our bodies are one piece and everything affects everything else. Piecemeal change only works if you're very observant about all the other things that change as you make your tweaks. Most people aren't that observant. A classic example is changing foot strike. You can land on your forefoot while continuing to over stride by changing how you hold your foot. Metatarsal stress fractures soon follow. You fix how your foot lands by changing things other than your foot, like your posture, or how you use your hips. All you do with your feet is ... nothing. You just let them flop around as they will. By the same token, all you really need to do to go uphill(or downhill) well is to lengthen your spine(including your neck) and widen your shoulders. Get your body in the right position and everything else will follow gracefully.