They will sleep in any conditions.
Laying down.
Yes..cows sleep. cows are mammals, all mammals sleep.
Cows sleep under a shed if they have one or they sleep outside depending on how much space you give them and where you let them sleep.
Cows sleep lying with their front feet folded under and their back legs tucked under them, but so that either the left or right hip is resting on the ground (which ever side they prefer to lay on)....
Yes they do!