Answer:
My second is performed by my first, and it is thought a thief by the marks of my whole might be caught.
What flies forever, rests never?
This dish is hot frankfurter served in a long, soft roll and typically topped with various condiments. Often served with hamburgers.
It covers you, you lose it every day and you'd die without it.
What comes down but never back goes up?
I am a animal that is cute but dangerous, what am I?