Which foot should be down, if any?
Usually your outside foot should be down, especially if you’re taking the turn at high speed (you need to lean more at higher speeds), with the intent being to avoid clipping the pedal. This is notably the exact opposite of what a lot of people seem to intuitively do, but is something that you will definately learn very quickly after the first time you clip a pedal.
If the ground is especially uneven though, having both feet at the same height is generally better for controlling your weight distribution. If cornering like this, usually you want the inside pedal to be the one to the front, as that will let you capture some of the extra energy of rebalancing after the turn to help maintain speed.
Where should one's weight be placed?
For a lower speed on even ground, normal weight placement for the bike type is fine and generally preferable.
For higher speeds or uneven ground, weight should be on your legs and arms but not the saddle, ideally with both your legs and arms slightly bent and loose so you can use them like shock absorbers. If the ground is level, you generally also want your weight back like you would position yourself while braking. The key here is to make sure you can shift your weight quickly to compensate for issues resulting from uneven ground, loss of traction, or other unforeseen complications.
Do you lean the bike? Lean the body? Lean both??
Both, but unless you are doing things strangely this will happen naturally (and you should let it). From an efficiency perspective, just leaning yourself is inefficient (you have to lean further to shift enough weight to turn properly), but from a safety perspective not leaning the bike is potentially dangerous because it puts a side load on the hub bearings and the wheels (good bikes should be fine, but it’s not something you should bet on, and the types of failure this can cause are both expensive to fix and really dangerous to have happen).
Is countersteering (the act of intentionally pointing the front wheel the opposite direction of the intended turn to initiate it) a good technique?
In general, you should countersteer as part of turning. It’s technically possible to turn without it (leaning appropriately to produce the same effect, sometimes called ‘counter-leaning’), but you need to know what you’re doing and it’s riskier than countersteering.
In practice though, if you have to think about countersteering, you’re probably approaching the process of turning incorrectly. The required motion is intuitive even to small children, and it’s instinctual enough to anyone who has ridden a bike any reasonable amount that they will generally not even notice that they’re doing it.
On level ground, a racing line is theoretically optimal but not the easiest. Outside of actual racing, you ideally want to just come from the outside, cut as close to the inside of the turn as possible, and end on the outside (this maximizes the turning radius, making it easier to safely turn at speed).
On inward banked turns (that is, the inner radius is lower than the outer), a similar out-in-out pattern is still safest, but it’s also relatively easy to take a constant distance from one edge if the bank angle is correct.
If you have to deal with an outward banked turn (that is, the outer radius is lower than the inner), a fixed distance from one edge is arguably safest.
Of course, that all assumes no potholes, bumps, or other hazards. Ideal line choice obviously avoids those.and is such that you maintain proper traction throughout the turn (though that is something you kind of have to learn based on the combination of tires and ground conditions). From a practical perspective, it’s very helpful to visualize the path you intend to take ahead of time.