lots of questions there!
Winter first- most adult butterflies die after a shoert period of two or three weeks on the wing. A few species hibernate such as the comma and orange tip but most spend the winter as eggs or pupae. For instance the black hairstreak is laid as an egg in late June/early July. The egg is laid on blackthorn and hatches in the spring. After a few weeks as a caterpillar it pupates and spends a short three weeks on the wing before dying. Overwintering butterflies find a dark place- deep amongst ivy for instance though man made structures provide warmth and dryness as well.
Butterflies and moths do sleep-or rest. Somewhere hidden away amongst foliage seems favourite. Dryness is required otherwise the wings get damaged- most rest up during rain and fly during dry weather.