subfloor repair

I have a very old house on a slab that is a rental. I have a little section of floor 4'x 4' in my entryway. Lifted up the tile and the concrete underneath was crumbly. Took out the concrete and now I'm down to wood planks. The wood floor is uneven - dips a good 2 inches from corner to corner - and the planks need to be secured. The rest of the room is carpeting. I'm sure I have some foundation problems but I'm not ready to tackle that.
Do I screw down the planks, then level with cement, then use 1/2" plywood before laying the tile? How do I get this even and create an even surface for the tiles? What kind of leveling cement do I use? I don't want it to crumble again.

Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
Add image file
Upload is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.