So Katt has been selling me paintings(that are not fake). After we trade then she will be really happy and sing the town tune. Does this mean my friendship is high with her?
I'd say probably! I don't know if the genuine nature of the paintings is just coincidence or if it is truly affected by your level of friendship, though. I also can't remember if uchis always sing after shadily selling/giving a player an item (I think they do?? Or at least most of the time??)
But even if neither of those things are truly special, you seem to be, in the least, pretty alright friends! Katt is my all-time favorite villager so I think of her as friendly, probably. Based on the wording of your question, I am going to assume you desire to have a level of high friendship with her (??)