I don't think it really matters what time but just make it consistent. I do mine after dinner. If I don't it during the day when lights are on and have been on for a while......
Yes your lights should run a daylight pattern. I run my lights from 10 am to 10 pm so at night I can see the tank. They should not be on all the time. Wouldn't worry to much about the trate just yet. You have a new tank and until it is established do sweat the trates as long as them are under 20ppm.
Whatcha gonna put in the tank?