Crouching is generally considered good for aiming, but i dunno if it's better to shoot a bow whilst standing tall of crouched... as far as why it makes you more powerful, doesn't make sense really - an arrow in the back is an arrow in the back, doesn't matter how you shot it - even if you were standing on your head or on one arm and pulled the string with your foot! It's still an arrow in the back...
It's generally considered that the lean stance for sneaking is best, couse you have better control over your body weight and balance, also it makes you less visible... foots steps can be a factor depending on the surface - wood, metal, stone, etc.
Metal plating armor is louder and gives you out, no doubt bout that... Leather armor is way more suitable for sneaking. Funny thing in oblivion was that you can just remover your shoes and sneak around silent while wearing a full set of steel armor
but i think we dive way too much in the realism factor, tbh