Root Intrusion in Bonus Room

Bought an old house. Half of carport was converted into a bonus/laundry room (~300 sq ft). They poured a concrete barrier *around* the slab (sticks up about 2" above slab and ~6" below).

Roots have grown down and the barrier and then up the gap between the original slab and new barrier.

I plan to trace these roots back and pull up whatever it is. After this, I'm stuck. How would you seal the gap the roots created? Pour more concrete in the gap? Use rubber sealant? Should I incorporate a vapor barrier? For the record, I want to do a concrete floor in here. Thanks

Bathroom where roots created a gap and caused water intrusion:
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Main space where gap is very large (I've seen insects crawling through the space): [/img]