Rust is easiest to spot up where the strings wind around the tuning pins. Rust weakens strings, making them more likely to break. If so, reject the piano. Broken strings can be replaced - in fact the entire piano can be restrung. Listen as you play each of the 88 keys .
All pianos go out of tune.
It's normal and unavoidable. But piano strings tend to go out of tune somewhat together. It's not normal to have a string that is wildly and disproportionately out of tune with respect to its neighboring strings. It suggests that the tuning pins might be too loose and may be slipping in the pinblock. Although everything can be fixed, I personally would never consider buying a piano with slipping tuning pins.