1. Twilight. Dusk. Sunset. Sunset would probably be the most exact. Twilight and dusk are more like longer periods of semi-darkness or fading light.
2. It's probably sarcastic, meaning that the person has done something deserving of scorn rather than a raise.
3. The USA (United States of America) is one country. If you are talking about the States as a collection of individual states, you might use "are". Depends on whether you want to empower the states or the federal government in your speech.
4. I say "my family is", because I regard my family as a unit. You can say "a family" or compare "one family" with "two families", so I'm going to say "family" is singular. If you are talking about the family as a group of individuals (which suggests a plural verb), then I would say "family members".