I think you'll find some variety here. I'm enough of a softy that despite carrying a tent with me, I'll also stay in motel a moderate amount of the time. However, there aren't always motels and so I'll also camp.
> What time you get up?
At US latitudes, I'll get up perhaps a little before sunrise and try to get on the road early. In fall or winter, I'll try to be on the road at first light. At further north latitudes, the sun might be up earlier but ~5am is early enough for me. The general idea is to get some early cycling in.
> Do you take your time at the campsite, or pack up and go?
Pack up and go. I can do that pretty quickly.
> Do you have breakfast, or just granola bar on the way?
I'll eat something no-cook at camp but wait 20-35 miles before having a real breakfast.
> What do you normally do for lunch? Quick sandwich, or pub/restaurant?
Restaurant at least 50% of the time.
> What time do you normally like to be at the next campsite?
I like to get in mid-afternoon. It also depends some on the trip. In a winter trip, it might be more like a 6:30am-5:00pm day including stops but in summer it might be closer to 5:30-3:00pm. That will vary some if there isn't a good spot to stay and I'll ride some extra. Similarly if I find a good spot at 1pm, I might just make it an earlier day.
> What kind of camping spot you think is best for a cyclo-tourist?
I'll do a little of everything. State parks are fine. Places that are too crowded with yahoos drinking and making noise through the night are not. Camping along the road not in official campsites is fine. A good motel is fine too. It also depends on the area. For example, I cycled one lap around Australia. In the outback I might camp not too far from where some caravans had an overnight pull-off sometimes and sometimes out in middle of nowhere. I also cycled across Russia. There we typically fetched water somewhere and then cycled ~10km to be away from any local villages. There wasn't a notion of campgrounds, but more pulling off the road and camping. The big trick in some spots was finding a place where ground was dry and not marshy.
> Do you take the panniers off and lock up your bikes, or just let your stuff sit there overnight? (I saw someone leave panniers on the bike, and I must admit I'm way too paranoid to do that).
Depends. Last night I made a short overnight trip to a nearby state park. Left panniers on the bike. Other times, I'll put them in the vestibule of my tent.
There is no right answer to these questions as much as different styles and preferences from different folks.