You could try some rapid set adhesive,goes off in a few hours but you have answered your own question in that you should really replace it even if it is just sprucing up for resale.
I use marmox quite a bit,easy to cut,lightweight and strong.
I get mine here
http://www.tilefixdirect.com/category/standard-tile-backer-insulation-boards.html?gclid=CKabgIDN5poCFQOuFQod6jl2CA
If they have only had one coat then they definatley needed more.
By coating before fixing it makes removing adhesive off the face easier.
Coating again before grout once again will make the grout clean off easier.
Then a final coat (I always do 2) to seal the grout.
Difficult to see in...
I very rarely use standard set but when I have you can still adjust tiles that were fitted in the morning at 3 in the afternoon.
Next day they were rock solid.
I wouldn't worry,when mixing just get it thick enough to maintain its shape when troweled.
Yes tank the shower area,1 meter up from tray,I normally tank before fitting the tray so it goes down behind it then plenty of silicone to seal where tray meets wall before tiling then silicone again when tiled.
Before the weather turned I was half way through building a shed dormer extension.Got the roof on and sides closed in and roof felted.
One half of the roof is wbp ply and the other half is structural spruce ply.
As its not insulated yet and there has been warm air from beneath there has been...
Most adhesive manufacturers recommend 15mm but most of the guys on here use 12mm for overboarding.
I have been using 6mm backerboards on jobs for quite a while now and have had no problems.
I prefer to not use mitres myself unless specified by a customer.
I find even with a new quaility blade the edges damage too easily.
I go for something like this
A previous job using this technique