I would recommend knocking all old tiles off, reboard with plasterboard and use a cement board in wet area/shower.
Doing this will give you a nice flat surface for you to start off.
As said in other posts use a cement based (powder) adhesive and mix with a paddle mixer in a flexi tub and make sure you follow mixing guides on the bag.
As with trowel size 10mm should be good as if you re board you will have a nice flat surface so you won’t have to pack out any tiles.
There's lots of alternatives but I'd get it from CTD Cardiff. It's not expensive. Tile Giant have it too or there's other slow set powders by other manufacturers such as BAL.
Ring them up,
Ask if its in stock
Ask how much is it
say "how much" in a loud voice
See what they'll do it for.
Should be under £18
Never take an on line price for something like this