Sagging 2nd floor and wet basement floor

Planning on buying a home in Brooklyn, House is approx. built in the 1920's, 16x36, 1 family, semi detached. After a walk thru and a home inspection a few major problems were noted.

1) On the 2nd floor, the corridor floor sag's significantly towards the entrance to the bathroom. It is very noticeable. The doors on the 2nd floor actually close themselves. Need some advice on what the problem can be.

2) Basement, unfinished concrete floor. After a rainstorm, under the stairs there was evidence of water. The floor was wet and the wood base of the stairs and other wood in contact with the floor is completed rotted and deteriorated. Did not see any leaks or evidence of any leaks from above. There is an nearby underground waste line. Could a leak from the waste line saturate the soil and foundation enough for water to penetrate thru? Need some advice on what the problem can be.

Thank you for your time.