The plumber will check how fast the pit fills in wet weather, test the float and check valve, and follow the discharge outside. On a septic property, expect questions about where the tank and leach field sit, so the water can be sent somewhere that drains away from both and from the foundation.
A new pit means cutting the floor, setting a liner, and running discharge piping through the wall. A dedicated circuit may involve the Wiring Inspector, and the Building Department has a Plumbing and Gas Inspector too, so ask which permits your job needs; in a mapped flood zone, add the Floodplain Permit to that question.
In VE or AE zones near the shore, a pump can't stop surge coming over the top. Ask about raising utilities and, on a sewered home, whether a backwater valve could help keep storm-driven water from pushing back through floor drains.