Sump Pump Installation
since the bsmt's ' finish'd ', you have to remove something to inspect the wall/floor junction to be certain - that's your call.
whether or not you install a sump & pump, without permeable soils/stone under the floor, the percolation rate of most soils would negate any efficiency of the pump in relieving ' hydrostatic pressure ' water,,, otoh, having 1 kind of covers your ***.
what's involved is breaking the floor - digging a pit - installing the sump - backfill w/clean #57 stone - install pump - hook up discharge - bolt down cover,,, plug in the pump ( we use only zoeller pumps ) - that's how we do it, anyway.
' drain tile ' refers to the outdat'd ' orangeburg ' clay pipe pieces but no one uses 'em anymore,,, 4" corrugat'd hdpe perforated pipe ( 100' rolls from an apron store ) is now std.