Why is "sta" used here to mean it is and not e' ?
Not quite sure, there is a slight difference in "sta" and "e". Maybe "sta' because it refers to a location?
My understanding is, stare is used to indicate location or state, essere (È) usually refers to the object or person directly. ex. 'Sono un'uomo' describes me as a man directly. 'Sto bene' describes the state I'm in.
Could this be translated as "he" or "she" is under the covers?
Accepted. NB not "undercover", which is sotto copertura.
"La coperta" ( plural: le coperte ) means "the blanket", but "il coperto" means "the cover".
Sotto le coperte means "under the blankets" - an idiom for "in bed".
This sentence is not right. The translation should be : He is probably under the blankets".
I think "sta" indicates an unusual or temporary location.