What he is referring to is Granite seam or repair resins, two manufactures are Chemorset or AKEMI . Stay away from polyester types of seam fillers for this as they has the tendency to rise up. So stick with the epoxy types if you are going to try using these for this.
ps.. these don't sand like...
Let your builder know what you are going to do with the room, also let him know what the max capacity ( ppl ) that you would ever see having in the room at any one time. Then have him take that info to his Structural Engineer and design the floor system. Yes it will be over engineered but it...
From a material stand point, it is possible to warp. Due to slate being from sedimentary rock it is within the realm of warping. I have had other sedimentary rocks ( tiles ) warp as fast as overnight ( but rare ). I would be more concerned with efflorescence ( leaching of minerals ) than warping.