Replacing an sink cabinet (48") with a double sink (36")
If height is an issue, use 1/4" concrete backer board, screwed and glued down on your floor. Be sure to use backer board screws and alternate seams so tiles won't crack or shift. If height is not an issue, use 1/2". Then, thinset your tiles on the backer board.

There shouldn't be any issue with the 12" cabinet. You could use a taller cabinet to create a division of workstations (stove/sink). You could have an open spice storage on the raised area on the stove side. The front could have a fake draw front on it.

Seems like no problem piping the double sink drains.