Hi Yorkie - Commiserations to your wife - the uncertainty is probably the worst thing of all. As Sqad has probably already mentioned, jaundice and raised LFTs can have a range of causes, and it sounds like they are trying to identify exactly what is the cause of these symptoms in your OH.
Hepatitis E is a rare variant virus, particularly in the UK. Usual cause is through ingestion of contaminated food or water, poor sanitation, occasionally thought to be transmitted from animals. Due to its rarity, it is not a virus that most hospital pathology labs are equipped to screen for , hence sending the sample off. Transport of the sample, sample preparation, testing, confirmation and sending the results out can take some while I am afraid.
The good news is that if it is confirmed as Hepatitis E, then although there are no specific treatments for Hep E, it does tend to spontaneously resolve after a couple of weeks or so. As with any incidence of viral hepatitis however, there is a small risk of serious health complications resulting from damage to the Liver.
As far as transmission of Hep E is concerned, that I am aware of, I cannot recall any documented instance of person to person transmission, so I think it unlikely that family / friends would need to be tested, unless they were exhibiting similar clinical symptoms. Good luck, and sorry if the above was not more helpful......