There are two main ones, Deformed Wing Virus (DWV) and K-wing.
https://beeinformed.org/2012/11/01/whats-wrong-with-my-hive/
DWV is much more common, but it can’t be treated, only prevented. It is caused by Varroa weakening the bees so that they can’t fight the virus. The only thing to do is treat the Varroa, and if you have DWV, you need to treat right now! If not, something like 90% of hives will die within 6 months. If she hasn’t treated for Varroa, this would be my top concern.
K-wing is a bit different and has a number of causes, including Nosema and tracheal mites. Nosema can be treated with thymol syrup. Tracheal mites probably get killed by Varroa treatments, but many experts recommend grease patties.
If she can send a photo of affected bees, we can help work out which it might be.
No idea, I have never tried it myself. It should help, but it will depend on the heat tolerance of the fermenting organisms, and also whether the honey gets re-exposed to the fermenting yeasts after opening it. After all, pasteurization only kills what is already in it. It doesn’t fix the water content problem. If more yeast drifts into it from the atmosphere when it is sitting open on the breakfast table, it could start fermenting again. 
Would love to see photos when you have it built. 