Maybe they finished the basement to quicken the sale of the house because, with the possible foundation problems, it wasn't selling before.
WHERE on the walls do you see the yellow stain? Top? Bottom? Middle?
You DO plan to have a good qualified house inspector examine the house before you make a commitment, don't you? And you DO plan to have him focus his attention on as much of the foundation as he can see, right? Even so, most house inspectors will disclaim responsibility for anything that is not visible.
The bowed wall is a concern. There is no such thing as "normal" bowing. If the stains are at the bottom of the walls, they're probably caused by water. The newly finished walls could easily be hiding mold, cracks, water entry, and who knows what else. Same with the new carpet.
If you REALLY REALLY want this house, after you get the inspection done, ask the owner very pointed questions about the basement, IN WRITING, and get the answers IN WRITING. If the owner balks at that, buy a different house.
Architect (NY) and Home Designer (PA)