No. Basically, and most of the time, it would be "her and me" or "she and I", depending on whether the people in the phrase are the subject or the object. She and I go to concerts together. Our...
Down-and-out is from a situation where a beaten prizefighter is knocked unconcious. It originated in 1889 in American English from pugilism (boxing or fist fighting).
Karst is a name for a certain type of landscape where the bedrock is riddled with cracks, fissures and caves formed by water dissolving/eroding the bedrock. "Of karstic origin" would refer to...