Can I fix this shower drain?

Hi, I am new here - hello to all of you. :-) I have had a shower leak, and I discovered that it was corrosion at the top inside of the drain, could even be where the pipe sleeves into another - so if the water backed up a little, it would start to leak. I want to change the drain (goes to a cast pipe I seem to recall when I repaired the ceiling below) and also make a bigger shower. So I have started to rip everything out. I would like to ask some questions if I may. 1. Will there be concrete across the entire tiled bathroom floor - I also want to extend the room.