Storm water drain system gets impacted because sometimes the asphalt shingle aggregate gets washed into the system. 

However, a solenoid leaking by or faulty humidistat will run excessive water down the drain constantly.

It cost me about $300 to drain and inspect a cess pool at one of our flips.

If you are located on shallow soil with lots of bedrock, building with a basement is both costly (drilling, blasting) and unwise {water often does not drain well from a rock bowl).  

Later the owner says no, she put in drains.

This will allow water to drain out of the horizontal rain screen and allow ventilation for faster drying. 

He's a great handyman, but never used him for drain plumbing before.

I know nothing about this trade of construction.Questions -*  Do you have to have a French drain (and are ALL interior drain systems called French drains or is there something specific to that) with a sump pump .... or can you have one without the other?

You may find that the "second bathroom" is only a toilet in the middle of the basement and IF there is a "shower", it's just a faucet on the wall near a floor drain.

It looks like it would need to be drained, cleaned, and possibly relined as part of the flip.