I have a flight at 6:30am when should I sleep the night before?

Tomorrow I'm taking my little sister to Dublin, Ireland for the day. We're flying from London, Luton at 6:30am and that means I will have to leave my house at 2am so I can collect my sister and arrive at the airport in good time. Our flight back isn't until 21:50 so it'll be a long, long day. We have a friend who's got a hotel so worst comes to worst we could always nap at his. What time should I go to sleep to ensure I feel rested? I can't sleep on planes and it's just over an hour and I'd feel moody. I could nap this afternoon but then I'm not sure if Ill be tired again come 6am.

Any ideas?

How do I find the average velocity of an airplane by year?

I want to compare how the top aircraft models have gotten faster year over year, or how airlines have changed their flight patterns to fly more quickly, but I can't find an average speed.

The National Transportation Safety board does annual accounts of car miles, but reports aircraft in hours flown. I want to know how many miles (rough estimate) yearly aircraft fly. My current idea is to multiply flight hours times average speed… But I can't find that anywhere!

Never been on a plane but parents want me to fly solo to Washington to visit grandparents?

My grandparents' 50th anniversary is coming up. Neither of my parents could get time off to visit, so they want to send me on a plane, by myself, from NY to Washington (state). The issue is that I've never once been on a plane, or even set foot in an airport, for that matter. I've voiced concerns about this with my parents but they don't care and say I'm going whether I like it or not. I'm 14 please help!

Tips on bring DSLR on a flight?

How does TSA/Airport security handle this? Chance of getting it stolen while being screened? Any concerns I should be worrying about?

Added (1). I'm thinking bringing a personal bag and a carry on bag. Will they allow putting my personal bag (camera equipment bag) inside my carry-on bag (backpack)?

How much should a decent round trip airline ticket cost?

A round trip airline ticket from Columbus, Ohio to Orlando, Florida, flying coach or economy? I don't fly enough to know a genuinely good price from a "too good to be true" or too expensive. Trying to decide whether it's worth it to just drive.