Are there any cultural differences between using the terms kvinna and dam? For example, lady can sometimes be quite a loaded term in English due to the connotations of chivalry, it can also be seen as a patronising term in some contexts. Does any of this carry over into Swedish culture or are they interchangeable terms? Are there also any age related usage to the terms (Calling older or younger women ladies)?
dam isn't really used in any context that isn't meant to be formal or extra polite. It's much more comparable to "gentleman" than to "lady" in that regard, since it doesn't have the potentially patronising connotation. (Or at least no more so than any other similar word said sneerily.) Both dam and kvinna are perfectly neutral, though.
You would also be much more likely to use dam as the age of the person goes up, as you probably guessed.