Lots of questions here.
I agree with your friend about the knees. Obviously your pedalling will be more efficient, with the force you are exerting transmitted more directly to the pedals, if your knees are moving in approximate alignment with the cranks. It'll be better for your knees, too - though clearly I'm not in a position to know whether you have any structural problem that might make it difficult for you. In the absence of such a problem, getting your saddle height correct might do it for you. You'll hear a lot of suggestions for how to do this. An easy way is to take off your shoes, sit in the saddle and place your unshod heel on the pedal. You should just - but only just - be able to keep your heel in contact with the pedal at the bottom of the downstroke. Adjust the saddle accordingly. You'll then find, with shoes on and your foot in the normal position, that there's just a slight bend in your knee at the bottom of the downstroke, which is as it should be.
Your toes sticking out to the sides sounds like it may be just the way you are - the opposite of pigeon-toed, no doubt there's a name for it. If that's the case, I wouldn't be forcing my feet into a (for you) unnatural position if I were you, doing so might set up all sorts of stresses that will cause you pain. Remember that when pedalling at 80 rpm you'll make more than 9000 revolutions in a two-hour ride. That's a lot of repetitions and it is best that your joints are moving along the line of least resistance. So while it would be ideal were your feet to be straighter on the pedals, don't force them to be so if it is uncomfortable.
Having said that, the purpose of the cages is twofold. First, they keep your foot in the correct position on the pedal. You should be pedalling with the ball of your foot above the pivot of the pedal. If you look at casual cyclists you'll frequently see them with the pedal under their instep, which is very inefficient and hard work. Equally, if you pedal with your toes, on tip-toe so to speak, your calves will be doing too much work instead of your quads, which will exhaust them and give you cramps. With the pedal forward in the three o'clock position, crank arm parallel to the ground, a plumb-line should ideally go from the tip of your kneecap through the ball of your foot to the pivot of the pedal - or thereabouts.
Second, the cage allows you to pedal more efficiently. When you say "scooping through on the upstroke" you have the right idea. Pedalling in circles rather than just up and down is the goal. People have different ways of describing it. Some compare the motion to that of wiping dirt off the sole of your shoe, others think of it as pedalling in squares - consciously moving your foot across the top of the stroke as well as down the far side. In practice what you are doing is aggressively "unweighting" the pedal on the upstroke, so that your other foot isn't effectively having to push against your own weight. The cage makes it possible to do this without losing contact with the pedal, by keeping your "unweighted" foot in place.
I hope this helps. I know it sounds complicated, but that's because I'm trying to describe things that are best experienced by feel, in practice. You can read all you like about the theory and practice of cycling, but it doesn't mean much until you're on the bike. Once you have the bike set up right, I'd recommend thinking like a golfer who keeps one swing thought in their head, to the exclusion of all else. In my case I used to just think about pedalling in circles. It's surprising how much difference that makes, and how soon the motion becomes second nature.