Learn English – “For both our sake” or “for both our sakes”

"Our bodies" refers to a collection of bodies owned by a group of people including the speaker. If a group of people share only a single body, then "our body" would be correct. When speaking of an actual physical body with an immune system, it's extremely rare for it to be occupied by more than one person.

"Each of [our|your] bodies" similarly refers to that same collection of bodies. As such it is still plural; even though it is encouraging us to consider every member individually in sequence, the end result is that we are considering the entire collection.

However, if you're referring to "the human body" as a generic construct as opposed to a group of specific people and their physical incarnations, that is an acceptable time to use the collective possessive form "our" and still use the singular "body":

Now consider humanity. Our body is a wonderful, complex thing. Our body's immune system alone is a system of such vast complexity that supercomputers only now are beginning to model it successfully.

Nope, it's definitely "For Heaven's Sake", as in "For the sake of Heaven". (Think "For God's Sake", "For Pete's Sake", etc.) The singular "sake" is the one that is the most standard and formal, though you also often see it as "For heaven's sakeS".

"For heaven sakes" is apparently one of the common alternate forms of the expression, but I imagine it is rather colloquial and region-dependent. I don't think I've ever heard it used, personally.