Are there any creatures based on breath or air, and specifically stealing these if possible?
The generic name for this would be Night Hag. There is sleep paralysis related folklore worldwide, some of which gave birth to what developed into the modern concept of the nightmare. I could not find any solid reference for the cat story.
Your mice can be found there:
In Eastern Chinese folklore, it is thought that a mouse can steal human breath at night. Human breath strengthens the mouse, allowing it longevity and the ability to briefly become human at night, in a similar fashion to fox spirits. The mouse sits near the person's face or under their nostrils
Some more samples:
In Scandinavian folklore, sleep paralysis is caused by a mare, a supernatural creature related to incubi and succubi. The mare is a damned woman, who is cursed and her body is carried mysteriously during sleep and without her noticing. In this state, she visits villagers to sit on their rib cages while they are asleep, causing them to experience nightmares.
In many parts of the Southern United States, the phenomenon is known as a hag, and the event is said to portend an approaching tragedy or accident
In Brazil, there is a legend about a mythological being called the pisadeira ("she who steps"). She is described as a tall, skinny old woman, with long dirty nails in dried toes, white tangled hair, a long nose, staring red eyes, and greenish teeth on her evil laugh. She lives over the roofs, waiting to step on the chest of those who sleep with a full stomach