Center of balance is (viewed from the side) ideally a straight line from the barbell down to mid foot. The genetic traits that affect the center of balance are primarily the length of the femur and the length of the torso. The longer the femur and the shorter the torso, the more forward lean will be necessary. The opposite is also true, the shorter the femur and the longer the torso, the less forward lean will occur.
Feet should at the very least be placed wide enough to allow the lifter to squat between their legs rather than behind them. If the squat is done behind the legs it's hard to hit correct depth and it often puts the lower back in a vulnerable position.
A wider foot position demands greater mobility. If the lifter can't squat below parallel with a wider style but want to increase the width of the stance, simply performing multiple sets with light weights (less than 70%) and gradually widen the stance over the course of several training sessions will typically be sufficient.
Depending on the mobility of the lifter, a slightly wider foot position can help too keep the lifter more upright. This must be determined individually.
A very wide stance put significant stress on the hips while a closer stance is typically associated with more stress on the legs.
While the angle of the feet (toes pointed out more or less) does play a role in muscle recruitment it should primarily be determined by where the lifter is most comfortable as long as the knees are able to track in the same direction as the toes and not cave in.
Foot placement should to a degree be evaluated based on deadlifting style. Someone who squats with a close stance, upright position might see carryover to- and from a deadlift that’s more leg dominant than back- and hip dominant. Similarly, a wide stance squatter can benefit from sumo deadlift.
The width of the hand placement is based on upper back mobility. A lifter with a tight back will not be able to use a close hand position. Doing so will typically result in a rounding of the back already during the descent. In that case, widen the hand position. The downside of a wide hand position is that it makes it harder to tighten the back properly.
A "suicide grip" is when the lifter place the thumbs on the same side as the other fingers. It can help to relieve stress on elbows and shoulders but is only used if the lifter have those issues.
You often hear terms such as "low bar" or "high bar" but let's ignore them for the simple reason that it's a continuum rather than two absolutes. In any case the bar should never be placed directly on a vertebrae but on a "shelf" of muscle created by pulling the shoulder blades back and down.
The lower the bar is placed, the more forward lean is necessary at maximal weights. The reason for this is because the center of balance shifts. Center of balance is (viewed from the side) ideally a straight line from the barbell down to mid foot. If the bar is more forward it shifts to the toes and if it's more back it shifts towards the heels. Since a squat is performed with at least some degree of "sitting back" which results in the torso leaning forward, the further down the bar is on the back, the more forward lean will be necessary to keep the center of balance on the mid foot.
There is no absolute right or wrong when it comes to forward lean other than most should strive to avoid the extremes (i.e. a squat that looks like a good morning or a completely upright position) since neither will allow the lifter to utilize the maximal amount of muscle.
Lifters with a high degree of forward lean will put more stress on their lower backs which often result in longer recovery times and can be dangerous.
The lower back is not the only body part in risk of injury. A low bar position combined with a too close hand placement can put significant stress on the arms and shoulders. It is often a cause of nagging shoulder injuries wrongly blamed on the bench press. Elbow injuries are also a risk, to the point it can be torn off.
Pay attention to these things because an injury that sets back a lifter a year is not worth 5 more kg on the bar. Those 5 kg are much better earned from training injury free that year.
Generally speaking the head should be placed so that the lifter looks forward or very slightly up or down. An aggressive "heads up" position results in unnecessary strain on the neck and can result in injuries. The eyes should be fixed and not allowed to wander during the lift.
When squatting down the knees and hip should for most people move in a concerted manner. Excessively sitting back takes away from the strong leg muscles and not sitting back at all takes away from the posterior chain. The knees should track the toes and not travel significantly more inward or outward. If the foot placement and center of balance is accounted for the path squatting down should occur naturally.
For powerlifting a squat should be to the depth of just below parallel. This is actually deeper than many think (where the crease of the hip is below the knee) but it’s not an “ass-to-grass” style squat.
Going too high is a self-explanatory issue in that it doesn't follow the rules of competition but going too deep is also an issue as it requires more energy to come up and thus make the lift harder than necessary. One solution is to widen the stance, making it harder to squat down too deep due to mobility restrictions. Another is obviously to simply tell the lifter to cut depth somewhat.
When reaching depth there should be no hesitation to stand up. Do not pause in the bottom. Some will benefit from "bouncing" in the bottom, making the getting up from the very bottom easier. If so, make sure to keep tightness throughout the entire lift. Others will be more comfortable squatting down more controlled and simply standing up. It's a matter of preference.
While squatting is generally considered a leg exercise, for powerlifters it's a full body lift. The back must be tight throughout the lift to not allow for any rounding. A tight back also helps to keep the spine from rounding.